From 9e6726a8606a3c5e1e9f31860e2fb5d85c5cc7c7 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 18:33:51 +0200
Subject: [PATCH 1/7] describe labels in suggestion form, add aria-invalid

---
 src/components/SuggestionForm.svelte | 44 +++++++++++++++++++++++++---
 1 file changed, 40 insertions(+), 4 deletions(-)

diff --git a/src/components/SuggestionForm.svelte b/src/components/SuggestionForm.svelte
index b13c181d..ba11e9c7 100644
--- a/src/components/SuggestionForm.svelte
+++ b/src/components/SuggestionForm.svelte
@@ -16,6 +16,10 @@
 	let url = $state('')
 	let sending = $state(false)
 
+	const TITLE_MAX_LENGTH = 50
+	const BODY_MAX_LENGTH = 10000
+	const NAME_MAX_LENGTH = 50
+
 	async function create_issue(e: SubmitEvent) {
 		e.preventDefault()
 
@@ -68,30 +72,47 @@
 
 	<form onsubmit={create_issue}>
 		<div class="form-group">
-			<label for="title">Short summary</label>
+			<label for="title">
+				<span>Short summary</span>
+				<span class="description">max. {TITLE_MAX_LENGTH} characters</span>
+			</label>
 			<input
 				type="text"
 				id="title"
 				class="full-width"
 				bind:value={title}
 				required
+				aria-invalid={title.length > TITLE_MAX_LENGTH}
 			/>
 		</div>
 
 		<div class="form-group">
-			<label for="body">Details</label>
+			<label for="body">
+				<span>Details</span>
+				<span class="description">max. {BODY_MAX_LENGTH} characters</span>
+			</label>
 			<textarea
 				id="body"
 				{@attach resize_textarea}
 				bind:value={body}
 				required
 				class="full-width"
+				aria-invalid={body.length > BODY_MAX_LENGTH}
 			></textarea>
 		</div>
 
 		<div class="form-group">
-			<label for="name">Your name (optional)</label>
-			<input type="text" id="name" bind:value={name} />
+			<label for="name">
+				<span>Your name</span>
+				<span class="description">optional</span>
+			</label>
+			<input
+				type="text"
+				id="name"
+				class="full-width"
+				bind:value={name}
+				aria-invalid={name.length > NAME_MAX_LENGTH}
+			/>
 		</div>
 
 		<button class="button" disabled={sending}>
@@ -133,4 +154,19 @@
 	.form-group {
 		margin-bottom: 1rem;
 	}
+
+	textarea {
+		height: 4lh;
+	}
+
+	label {
+		display: flex;
+		justify-content: space-between;
+		align-items: end;
+
+		.description {
+			font-size: 0.875rem;
+			color: var(--secondary-text-color);
+		}
+	}
 </style>

From cce839a86363a01d16b3482ce1f93c161fd4760c Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 18:34:29 +0200
Subject: [PATCH 2/7] remove notice

---
 src/routes/+page.svelte | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/src/routes/+page.svelte b/src/routes/+page.svelte
index f07f6bb2..fb6286cd 100644
--- a/src/routes/+page.svelte
+++ b/src/routes/+page.svelte
@@ -111,11 +111,6 @@
 	</article>
 </div>
 
-<p>
-	Note that this project is still in its early stages. Breaking changes are likely, and
-	the structure of the application and the database may change without notice.
-</p>
-
 <style>
 	.features {
 		margin-block: 2rem;

From 6c941098630f8c94e683e0f3eacb5a3c19766fe0 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 18:38:02 +0200
Subject: [PATCH 3/7] add comments to global css file

---
 src/routes/app.css | 114 +++++++++++++++++++++++++--------------------
 1 file changed, 63 insertions(+), 51 deletions(-)

diff --git a/src/routes/app.css b/src/routes/app.css
index ac9d9ac5..870eb36c 100644
--- a/src/routes/app.css
+++ b/src/routes/app.css
@@ -1,3 +1,5 @@
+/* global stuff */
+
 @font-face {
 	font-family: 'DM Mono';
 	font-style: normal;
@@ -47,6 +49,8 @@ body[data-theme='dark'] {
 	--card-shadow: #ffffff06;
 }
 
+/* body */
+
 body {
 	font-family:
 		'Lucida Sans', 'Lucida Sans Regular', 'Lucida Grande', 'Lucida Sans Unicode',
@@ -57,6 +61,10 @@ body {
 	line-height: 1.5;
 }
 
+body:has(#nav_dialog[open]) {
+	overflow: hidden;
+}
+
 @media (prefers-reduced-motion: no-preference) {
 	body,
 	html {
@@ -64,6 +72,29 @@ body {
 	}
 }
 
+/* headings */
+
+h1,
+h2,
+h3 {
+	line-height: 1.2;
+	font-weight: 500;
+	color: var(--heading-color);
+	font-family: 'DM Mono', monospace;
+}
+
+h2 {
+	font-size: 1.875rem;
+	margin-block: 0.5rem 1rem;
+}
+
+h3 {
+	font-size: 1.45rem;
+	margin-block: 2rem 1rem;
+}
+
+/* various elements */
+
 p {
 	margin-block: 1rem;
 }
@@ -90,30 +121,6 @@ strong {
 	font-weight: 600;
 }
 
-h1,
-h2,
-h3 {
-	line-height: 1.2;
-	font-weight: 500;
-	color: var(--heading-color);
-	font-family: 'DM Mono', monospace;
-}
-
-h2 {
-	font-size: 1.875rem;
-	margin-block: 0.5rem 1rem;
-}
-
-h3 {
-	font-size: 1.45rem;
-	margin-block: 2rem 1rem;
-}
-
-.hint {
-	color: var(--secondary-text-color);
-	font-size: 1rem;
-}
-
 ul {
 	padding-left: 1.5rem;
 
@@ -132,6 +139,27 @@ ol {
 	}
 }
 
+dialog {
+	font: inherit;
+	color: inherit;
+	background: none;
+	outline: none;
+	border: none;
+	width: 100%;
+}
+
+/* interactive elements */
+
+summary {
+	cursor: pointer;
+	width: fit-content;
+
+	&:focus-visible {
+		outline: 1px solid var(--text-color);
+		outline-offset: 2px;
+	}
+}
+
 button,
 input,
 select,
@@ -174,12 +202,6 @@ input[type='search']::-ms-clear {
 	display: none;
 }
 
-label {
-	display: block;
-	margin-bottom: 0.1rem;
-	font-size: 1rem;
-}
-
 button:not(:disabled) {
 	cursor: pointer;
 }
@@ -206,6 +228,14 @@ a.button {
 	display: inline-block;
 }
 
+label {
+	display: block;
+	margin-bottom: 0.1rem;
+	font-size: 1rem;
+}
+
+/* utility classes */
+
 .visually-hidden {
 	position: absolute;
 	clip: rect(1px, 1px, 1px, 1px);
@@ -221,25 +251,7 @@ a.button {
 	width: 100%;
 }
 
-summary {
-	cursor: pointer;
-	width: fit-content;
-
-	&:focus-visible {
-		outline: 1px solid var(--text-color);
-		outline-offset: 2px;
-	}
-}
-
-dialog {
-	font: inherit;
-	color: inherit;
-	background: none;
-	outline: none;
-	border: none;
-	width: 100%;
-}
-
-body:has(#nav_dialog[open]) {
-	overflow: hidden;
+.hint {
+	color: var(--secondary-text-color);
+	font-size: 1rem;
 }

From 6467ecaf870c20453b655d2d99d96983adce3c86 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 18:53:35 +0200
Subject: [PATCH 4/7] add icons to footer items

---
 src/components/Footer.svelte    | 43 +++++++++++++++++++++++++++++----
 src/components/NavMobile.svelte | 16 +++++++++++-
 2 files changed, 53 insertions(+), 6 deletions(-)

diff --git a/src/components/Footer.svelte b/src/components/Footer.svelte
index e21b900c..8cd2f3e1 100644
--- a/src/components/Footer.svelte
+++ b/src/components/Footer.svelte
@@ -1,14 +1,47 @@
+<script lang="ts">
+	import {
+		faBook,
+		faCog,
+		faCubes,
+		faPuzzlePiece,
+	} from '@fortawesome/free-solid-svg-icons'
+
+	import { faPenToSquare } from '@fortawesome/free-regular-svg-icons'
+	import Fa from 'svelte-fa'
+</script>
+
 <footer class="hint">
-	<a href="/contribute">Contribute</a>
-	<a href="/settings">Settings</a>
-	<a href="/missing">Missing data</a>
-	<a href="/resources">Resources</a>
-	<a href="/foundations">Foundations</a>
+	<ul>
+		<li>
+			<Fa icon={faPenToSquare} scale={0.875} />
+			<a href="/contribute">Contribute</a>
+		</li>
+		<li>
+			<Fa icon={faCog} scale={0.875} />
+			<a href="/settings">Settings</a>
+		</li>
+		<li>
+			<Fa icon={faPuzzlePiece} scale={0.875} />
+			<a href="/missing">Missing data</a>
+		</li>
+		<li>
+			<Fa icon={faBook} scale={0.875} />
+			<a href="/resources">Resources</a>
+		</li>
+		<li>
+			<Fa icon={faCubes} scale={0.875} />
+			<a href="/foundations">Foundations</a>
+		</li>
+	</ul>
 </footer>
 
 <style>
 	footer {
 		margin-bottom: 1.5rem;
+	}
+
+	ul {
+		list-style-type: none;
 		display: flex;
 		justify-content: center;
 		flex-wrap: wrap;
diff --git a/src/components/NavMobile.svelte b/src/components/NavMobile.svelte
index 14bcf0e3..a13c1d8c 100644
--- a/src/components/NavMobile.svelte
+++ b/src/components/NavMobile.svelte
@@ -1,11 +1,16 @@
 <script lang="ts">
 	import type { Structure } from '$lib/commons/types'
+	import { faPenToSquare } from '@fortawesome/free-regular-svg-icons'
 	import {
 		faArrowsSplitUpAndLeft,
+		faBook,
 		faChartBar,
+		faCog,
+		faCubes,
 		faDatabase,
 		faHome,
 		faList,
+		faPuzzlePiece,
 		faSearch,
 		faXmark,
 	} from '@fortawesome/free-solid-svg-icons'
@@ -98,18 +103,23 @@
 	<ul class="secondary-list">
 		<li>
 			<a href="/contribute">Contribute</a>
+			<Fa icon={faPenToSquare} scale={0.875} />
 		</li>
 		<li>
 			<a href="/settings">Settings</a>
+			<Fa icon={faCog} scale={0.875} />
 		</li>
 		<li>
-			<a href="/missing">Missing Data</a>
+			<a href="/missing">Missing data</a>
+			<Fa icon={faPuzzlePiece} scale={0.875} />
 		</li>
 		<li>
 			<a href="/resources">Resources</a>
+			<Fa icon={faBook} scale={0.875} />
 		</li>
 		<li>
 			<a href="/foundations">Foundations</a>
+			<Fa icon={faCubes} scale={0.875} />
 		</li>
 	</ul>
 </nav>
@@ -151,5 +161,9 @@
 
 	ul.secondary-list {
 		color: var(--secondary-text-color);
+
+		li {
+			margin-bottom: 0.25rem;
+		}
 	}
 </style>

From aed2ce7802cf778a4b49835bf71898bd3af9ee4a Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 19:17:09 +0200
Subject: [PATCH 5/7] use markdown to render foundations page

---
 .vscode/settings.json                  |  5 ++
 package.json                           |  2 +
 pnpm-lock.yaml                         | 71 ++++++++++++++++++++++++++
 src/lib/content/foundations.md         | 31 +++++++++++
 src/lib/server/rendering.ts            | 16 ++++++
 src/routes/foundations/+page.server.ts | 25 ++-------
 src/routes/foundations/+page.svelte    |  6 +--
 7 files changed, 130 insertions(+), 26 deletions(-)
 create mode 100644 src/lib/content/foundations.md

diff --git a/.vscode/settings.json b/.vscode/settings.json
index 1fd0af92..f8d45339 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -92,6 +92,7 @@
 		"diffeomorphisms",
 		"dualizable",
 		"Dualization",
+		"endofunctors",
 		"Engelking",
 		"epimorphic",
 		"epimorphism",
@@ -113,6 +114,10 @@
 		"Haus",
 		"Heyting",
 		"homotopy",
+		"hypercategories",
+		"hypercategory",
+		"hypercollection",
+		"hypercollections",
 		"infima",
 		"infimum",
 		"infinitary",
diff --git a/package.json b/package.json
index 964c01a1..14bbe2d0 100644
--- a/package.json
+++ b/package.json
@@ -28,6 +28,7 @@
 		"@sveltejs/kit": "^2.55.0",
 		"@sveltejs/vite-plugin-svelte": "^7.0.0",
 		"@types/katex": "^0.16.8",
+		"@types/markdown-it": "^14.1.2",
 		"@types/node": "^25.5.0",
 		"chokidar": "^5.0.0",
 		"dotenv": "^17.3.1",
@@ -53,6 +54,7 @@
 		"ioredis": "^5.10.1",
 		"katex": "^0.16.44",
 		"leo-profanity": "^1.9.0",
+		"markdown-it": "^14.1.1",
 		"sql-template-tag": "^5.2.1",
 		"svelte-chartjs": "^4.0.1",
 		"svelte-fa": "^4.0.4"
diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml
index 91769b90..644a6df0 100644
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@@ -39,6 +39,9 @@ importers:
       leo-profanity:
         specifier: ^1.9.0
         version: 1.9.0
+      markdown-it:
+        specifier: ^14.1.1
+        version: 14.1.1
       sql-template-tag:
         specifier: ^5.2.1
         version: 5.2.1
@@ -61,6 +64,9 @@ importers:
       '@types/katex':
         specifier: ^0.16.8
         version: 0.16.8
+      '@types/markdown-it':
+        specifier: ^14.1.2
+        version: 14.1.2
       '@types/node':
         specifier: ^25.5.0
         version: 25.5.0
@@ -763,6 +769,15 @@ packages:
   '@types/katex@0.16.8':
     resolution: {integrity: sha512-trgaNyfU+Xh2Tc+ABIb44a5AYUpicB3uwirOioeOkNPPbmgRNtcWyDeeFRzjPZENO9Vq8gvVqfhaaXWLlevVwg==}
 
+  '@types/linkify-it@5.0.0':
+    resolution: {integrity: sha512-sVDA58zAw4eWAffKOaQH5/5j3XeayukzDk+ewSsnv3p4yJEZHCCzMDiZM8e0OUrRvmpGZ85jf4yDHkHsgBNr9Q==}
+
+  '@types/markdown-it@14.1.2':
+    resolution: {integrity: sha512-promo4eFwuiW+TfGxhi+0x3czqTYJkG8qB17ZUJiVF10Xm7NLVRSLUsfRTU/6h1e24VvRnXCx+hG7li58lkzog==}
+
+  '@types/mdurl@2.0.0':
+    resolution: {integrity: sha512-RGdgjQUZba5p6QEFAVx2OGb8rQDL/cPRG7GiedRzMcJ1tYnUANBncjbSB1NRGwbvjcPeikRABz2nshyPk1bhWg==}
+
   '@types/node@25.5.0':
     resolution: {integrity: sha512-jp2P3tQMSxWugkCUKLRPVUpGaL5MVFwF8RDuSRztfwgN1wmqJeMSbKlnEtQqU8UrhTmzEmZdu2I6v2dpp7XIxw==}
 
@@ -781,6 +796,9 @@ packages:
     engines: {node: '>=0.4.0'}
     hasBin: true
 
+  argparse@2.0.1:
+    resolution: {integrity: sha512-8+9WqebbFzpX9OR+Wa6O29asIogeRMzcGtAINdpMHHyAg10f05aSFVBbcEqGf/PXw1EjAZ+q2/bEBg3DvurK3Q==}
+
   aria-query@5.3.1:
     resolution: {integrity: sha512-Z/ZeOgVl7bcSYZ/u/rh0fOpvEpq//LZmdbkXyc7syVzjPAhfOa9ebsdTSjEBDU4vs5nC98Kfduj1uFo0qyET3g==}
     engines: {node: '>= 0.4'}
@@ -859,6 +877,10 @@ packages:
     resolution: {integrity: sha512-IO8C/dzEb6O3F9/twg6ZLXz164a2fhTnEWb95H23Dm4OuN+92NmEAlTrupP9VW6Jm3sO26tQlqyvyi4CsnY9GA==}
     engines: {node: '>=12'}
 
+  entities@4.5.0:
+    resolution: {integrity: sha512-V0hjH4dGPh9Ao5p0MoRY6BVqtwCjhz6vI5LT8AJ55H+4g9/4vbHx1I54fS0XuclLhDHArPQCiMjDxjaL8fPxhw==}
+    engines: {node: '>=0.12'}
+
   es6-crawler-detect@4.0.2:
     resolution: {integrity: sha512-ET8rHP97ifJtkImZJ6Pul/mB25hEKQNSVM592pWmeumu3DBJ+LnhVWDahfsgbjvZL/78W4EupYPBAZijbwPi4g==}
 
@@ -1022,6 +1044,9 @@ packages:
     resolution: {integrity: sha512-NXYBzinNrblfraPGyrbPoD19C1h9lfI/1mzgWYvXUTe414Gz/X1FD2XBZSZM7rRTrMA8JL3OtAaGifrIKhQ5yQ==}
     engines: {node: '>= 12.0.0'}
 
+  linkify-it@5.0.0:
+    resolution: {integrity: sha512-5aHCbzQRADcdP+ATqnDuhhJ/MRIqDkZX5pyjFHRRysS8vZ5AbqGEoFIb6pYHPZ+L/OC2Lc+xT8uHVVR5CAK/wQ==}
+
   locate-character@3.0.0:
     resolution: {integrity: sha512-SW13ws7BjaeJ6p7Q6CO2nchbYEc3X3J6WrmTTDto7yMPqVSZTUyY5Tjbid+Ab8gLnATtygYtiDIJGQRRn2ZOiA==}
 
@@ -1034,6 +1059,13 @@ packages:
   magic-string@0.30.21:
     resolution: {integrity: sha512-vd2F4YUyEXKGcLHoq+TEyCjxueSeHnFxyyjNp80yg0XV4vUhnDer/lvvlqM/arB5bXQN5K2/3oinyCRyx8T2CQ==}
 
+  markdown-it@14.1.1:
+    resolution: {integrity: sha512-BuU2qnTti9YKgK5N+IeMubp14ZUKUUw7yeJbkjtosvHiP0AZ5c8IAgEMk79D0eC8F23r4Ac/q8cAIFdm2FtyoA==}
+    hasBin: true
+
+  mdurl@2.0.0:
+    resolution: {integrity: sha512-Lf+9+2r+Tdp5wXDXC4PcIBjTDtq4UKjCPMQhKIuzpJNW0b96kVqSwW0bT7FhRSfmAiFYgP+SCRvdrDozfh0U5w==}
+
   mri@1.2.0:
     resolution: {integrity: sha512-tzzskb3bG8LvYGFF/mDTpq3jpI6Q9wc3LEmBaghu+DdCssd1FakN7Bc0hVNmEyGq1bq3RgfkCb3cmQLpNPOroA==}
     engines: {node: '>=4'}
@@ -1096,6 +1128,10 @@ packages:
   promise-limit@2.7.0:
     resolution: {integrity: sha512-7nJ6v5lnJsXwGprnGXga4wx6d1POjvi5Qmf1ivTRxTjH4Z/9Czja/UCMLVmB9N93GeWOU93XaFaEt6jbuoagNw==}
 
+  punycode.js@2.3.1:
+    resolution: {integrity: sha512-uxFIHU0YlHYhDQtV4R9J6a52SLx28BCjT+4ieh7IGbgwVJWO+km431c4yRlREUAsAmt/uMjQUyQHNEPf0M39CA==}
+    engines: {node: '>=6'}
+
   readdirp@4.1.2:
     resolution: {integrity: sha512-GDhwkLfywWL2s6vEjyhri+eXmfH6j1L7JE27WhqLeYzoh/A3DBaYGEj2H/HFZCn/kMfim73FXxEJTw06WtxQwg==}
     engines: {node: '>= 14.18.0'}
@@ -1197,6 +1233,9 @@ packages:
     engines: {node: '>=14.17'}
     hasBin: true
 
+  uc.micro@2.1.0:
+    resolution: {integrity: sha512-ARDJmphmdvUk6Glw7y9DQ2bFkKBHwQHLi2lsaH6PPmz/Ka9sFOBsBluozhDltWmnv9u/cF6Rt87znRTPV+yp/A==}
+
   undici-types@7.18.2:
     resolution: {integrity: sha512-AsuCzffGHJybSaRrmr5eHr81mwJU3kjw6M+uprWvCXiNeN9SOGwQ3Jn8jb8m3Z6izVgknn1R0FTCEAP2QrLY/w==}
 
@@ -1807,6 +1846,15 @@ snapshots:
 
   '@types/katex@0.16.8': {}
 
+  '@types/linkify-it@5.0.0': {}
+
+  '@types/markdown-it@14.1.2':
+    dependencies:
+      '@types/linkify-it': 5.0.0
+      '@types/mdurl': 2.0.0
+
+  '@types/mdurl@2.0.0': {}
+
   '@types/node@25.5.0':
     dependencies:
       undici-types: 7.18.2
@@ -1821,6 +1869,8 @@ snapshots:
 
   acorn@8.16.0: {}
 
+  argparse@2.0.1: {}
+
   aria-query@5.3.1: {}
 
   axobject-query@4.1.0: {}
@@ -1871,6 +1921,8 @@ snapshots:
 
   dotenv@17.3.1: {}
 
+  entities@4.5.0: {}
+
   es6-crawler-detect@4.0.2: {}
 
   esbuild@0.25.12:
@@ -2065,6 +2117,10 @@ snapshots:
       lightningcss-win32-arm64-msvc: 1.32.0
       lightningcss-win32-x64-msvc: 1.32.0
 
+  linkify-it@5.0.0:
+    dependencies:
+      uc.micro: 2.1.0
+
   locate-character@3.0.0: {}
 
   lodash.defaults@4.2.0: {}
@@ -2075,6 +2131,17 @@ snapshots:
     dependencies:
       '@jridgewell/sourcemap-codec': 1.5.5
 
+  markdown-it@14.1.1:
+    dependencies:
+      argparse: 2.0.1
+      entities: 4.5.0
+      linkify-it: 5.0.0
+      mdurl: 2.0.0
+      punycode.js: 2.3.1
+      uc.micro: 2.1.0
+
+  mdurl@2.0.0: {}
+
   mri@1.2.0: {}
 
   mrmime@2.0.1: {}
@@ -2116,6 +2183,8 @@ snapshots:
 
   promise-limit@2.7.0: {}
 
+  punycode.js@2.3.1: {}
+
   readdirp@4.1.2: {}
 
   readdirp@5.0.0: {}
@@ -2236,6 +2305,8 @@ snapshots:
 
   typescript@5.9.3: {}
 
+  uc.micro@2.1.0: {}
+
   undici-types@7.18.2: {}
 
   universal-github-app-jwt@2.2.2: {}
diff --git a/src/lib/content/foundations.md b/src/lib/content/foundations.md
new file mode 100644
index 00000000..ff158664
--- /dev/null
+++ b/src/lib/content/foundations.md
@@ -0,0 +1,31 @@
+## Foundations
+
+In _CatDat_, we work with the following convenient set-theoretic foundation for category theory.
+
+We work with ZFC and two Grothendieck universes $U \in U^+$. So in principle everything is a set, but we will rename them as follows to introduce three levels of size: the sets in $U$ are renamed to _sets_ (sometimes for clarity: _small sets_), the sets in $U^+$ are renamed to _collections_ (sometimes also called _large sets_), and all sets are renamed to _hypercollections_ (which may or may not lie in $U^+$).
+
+For example, $\mathbb{R}$ is a set, $U$ is a collection, and $U^+$ is a hypercollection. The collection $U$ consists of all sets, and the hypercollection $U^+$ consists of all collections. Every set is also a collection, and every collection is also a hypercollection.
+
+Note that sets, collections, and hypercollections all satisfy the ZFC axioms. In this sense, (hyper-)collections behave in the same way as sets. This is crucial for category theory. For example, we can form the collection of all maps between two collections. Just imagine three levels of ZFC on top of each other. Grothendieck universes are just an implementation detail, which we can _and will_ drop from now on. Sets are on level 1, collections on level 2, and hypercollections on level 3. You can imagine concrete mathematical objects like numbers or functions as being on level 0 (even though they are usually modeled as sets in ZFC).
+
+A _category_ $\mathcal{C}$ is defined as a pair of collections $O,M$, whose elements are called _objects_ resp. _morphisms_, together with maps $i : O \to M$ (_identity_), $s : M \to O$ (_source_), $t : M \to O$ (_target_) as well as $c : M \times_O M \to M$ (_composition_), and the usual category axioms need to be satisfied. The domain of $c$ consists of all pairs of morphisms $(f,g)$ with $s(f)=t(g)$, and we always write $f \circ g := c(f,g)$ for their composition. Instead of $i(X)$ one usually writes $\mathrm{id}_X$ for the identity morphism of $X$.
+
+When $X \in O$ is an object, it is common to write $X \in \mathcal{C}$. When $f \in M$ is a morphism and $s(f) = X$, $t(f) = Y$, we write $f : X \to Y$. We write $\mathrm{Hom}(X,Y)$ for the collection of such morphisms with source $X$ and target $Y$. It is not necessarily a set. If this collection is a set for all $X,Y$, the category is called _locally small_.
+
+A _small category_ is defined as above, just by using _sets_ $O$ and $M$ (instead of collections). A _hypercategory_ is also defined in the same way, but by using _hypercollections_ $O$ and $M$ (instead of collections). Every small category is also a category, and every category is also a hypercategory.
+
+Functors $\mathcal{C} \to \mathcal{C}'$ between all types of categories are defined as in every textbook on category theory; they are given by two maps $O \to O'$, $M \to M'$, etc. Between two categories there is a collection of all functors, in the same way that between two small categories there is a set of all functors.
+
+The category of sets $\mathbf{Set}$ is defined by using the collection of all sets as objects (aka small sets). The category of groups $\mathbf{Grp}$ uses the collection of all groups (aka small groups). We can also construct the category $\mathbf{Cat}$ of small categories, etc. All these are locally small.
+
+If $\mathcal{C}, \mathcal{D}$ are two categories, we can construct the functor category $[\mathcal{C}, \mathcal{D}]$ as usual (there is simply no set-theoretic issue since collections behave just like sets). If $\mathcal{C}$ is small and $\mathcal{D}$ is locally small, then $[\mathcal{C}, \mathcal{D}]$ is locally small. This extra assumption on $\mathcal{C}$ is one of many indicators why categories should not be assumed to be locally small by default. We could not even talk about the category of endofunctors of a general locally small category, so there would certainly be no category of monads. It is better to explicitly say when we need the assumption of being locally small.
+
+The collections form a hypercategory $\mathbf{Set}^+$. Likewise, we have a hypercategory $\mathbf{Cat}^+$ consisting of all categories. For instance, $\mathbf{Set}$ is an object of $\mathbf{Cat}^+$, but not of $\mathbf{Cat}$. In our framework, we have no way to group all hypercollections (or even all hypercategories) into a single mathematical object; for this we would need a third Grothendieck universe, but usually this grouping is not required anyway.
+
+If $\mathcal{C}$ is any category and $A \in \mathcal{C}$ is an object, we have the Hom-functor $\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}^+$ defined as usual, but notice that it takes values in the hypercategory of all collections. The Yoneda Lemma and all of its corollaries can be proven as usual without ever assuming that $\mathcal{C}$ is locally small. But if that happens to be the case, we get $\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}$, the target being a category.
+
+We may define _adjunctions_ as usual: we require natural isomorphisms $\mathrm{Hom}(F(A),B) \cong \mathrm{Hom}(A,G(B))$ of functors valued in $\mathbf{Set}^+$. We do not need to assume the categories to be locally small.
+
+If $A$ is an object, the collection of all monomorphisms $B \to A$ does not need to be a set. But if (for every choice of $A$) there is a set of such monomorphisms such that every monomorphism $B \to A$ is isomorphic over $A$ to one in the set, then the category is called _well-powered_. The dual notion of being _well-copowered_ is defined in the same way by using epimorphisms $A \to B$. Every small category is well-powered, but there are many well-powered categories that are not small.
+
+There is a lot more to say about the set-theoretic foundations of category theory (in fact, many papers have been written on the subject, and the approach developed above is just _one_ of [many](https://xkcd.com/927/) approaches), but this should be sufficient for the purposes of _CatDat_.
diff --git a/src/lib/server/rendering.ts b/src/lib/server/rendering.ts
index 26daa7ef..15e3e046 100644
--- a/src/lib/server/rendering.ts
+++ b/src/lib/server/rendering.ts
@@ -1,5 +1,6 @@
 import katex from 'katex'
 import { is_object } from './utils'
+import MarkdownIt from 'markdown-it'
 
 function render_formula(formula: string): string {
 	return katex.renderToString(formula, {
@@ -36,3 +37,18 @@ export function render_nested_formulas<T>(obj: T): T {
 
 	return obj
 }
+
+const md = new MarkdownIt()
+
+const content_dict = import.meta.glob('$lib/content/*.md', {
+	query: '?raw',
+	import: 'default',
+	eager: true,
+}) as Record<string, string>
+
+export function get_rendered_content(file: string) {
+	const key = `/src/lib/content/${file}.md`
+	const txt = content_dict[key]
+	const html = md.render(txt)
+	return render_formulas(html)
+}
diff --git a/src/routes/foundations/+page.server.ts b/src/routes/foundations/+page.server.ts
index 7850c8c5..7fef77fd 100644
--- a/src/routes/foundations/+page.server.ts
+++ b/src/routes/foundations/+page.server.ts
@@ -1,23 +1,6 @@
-import { render_nested_formulas } from '$lib/server/rendering'
+import { get_rendered_content } from '$lib/server/rendering'
 
-const foundations = [
-	'In <i>CatDat</i>, we work with the following convenient set-theoretic foundation for category theory.',
-	'We work with ZFC and two Grothendieck universes $U \\in U^+$. So in principle everything is a set, but we will rename them as follows to introduce three levels of size: the sets in $U$ are renamed to <i>sets</i> (sometimes for clarity: <i>small sets</i>), the sets in $U^+$ are renamed to <i>collections</i> (sometimes also called <i>large sets</i>), and all sets are renamed to <i>hypercollections</i> (which may or may not lie in $U^+$).',
-	'For example, $\\mathbb{R}$ is a set, $U$ is a collection, and $U^+$ is a hypercollection. The collection $U$ consists of all sets, and the hypercollection $U^+$ consists of all collections. Every set is also a collection, and every collection is also a hypercollection.',
-	'Note that sets, collections, and hypercollections all satisfy the ZFC axioms. In this sense, (hyper-)collections behave in the same way as sets. This is crucial for category theory. For example, we can form the collection of all maps between two collections. Just imagine three levels of ZFC on top of each other. Grothendieck universes are just an implementation detail, which we can <i>and will</i> drop from now on. Sets are on level 1, collections on level 2, and hypercollections on level 3. You can imagine concrete mathematical objects like numbers or functions as being on level 0 (even though they are usually modeled as sets in ZFC).',
-	'A <i>category</i> $\\mathcal{C}$ is defined as a pair of collections $O,M$, whose elements are called <i>objects</i> resp. <i>morphisms</i>, together with maps $i : O \\to M$ (<i>identity</i>), $s : M \\to O$ (<i>source</i>), $t : M \\to O$ (<i>target</i>) as well as $c : M \\times_O M \\to M$ (<i>composition</i>), and the usual category axioms need to be satisfied. The domain of $c$ consists of all pairs of morphisms $(f,g)$ with $s(f)=t(g)$, and we always write $f \\circ g := c(f,g)$ for their composition. Instead of $i(X)$ one usually writes $\\mathrm{id}_X$ for the identity morphism of $X$.',
-	'When $X \\in O$ is an object, it is common to write $X \\in \\mathcal{C}$. When $f \\in M$ is a morphism and $s(f) = X$, $t(f) = Y$, we write $f : X \\to Y$. We write $\\mathrm{Hom}(X,Y)$ for the collection of such morphisms with source $X$ and target $Y$. It is not necessarily a set. If this collection is a set for all $X,Y$, the category is called <i>locally small</i>.',
-	'A <i>small category</i> is defined as above, just by using <i>sets</i> $O$ and $M$ (instead of collections). A <i>hypercategory</i> is also defined in the same way, but by using <i>hypercollections</i> $O$ and $M$ (instead of collections). Every small category is also a category, and every category is also a hypercategory.',
-	"Functors $\\mathcal{C} \\to \\mathcal{C}'$ between all types of categories are defined as in every textbook on category theory; they are given by two maps $O \\to O'$, $M \\to M'$, etc. Between two categories there is a collection of all functors, in the same way that between two small categories there is a set of all functors.",
-	'The category of sets $\\mathbf{Set}$ is defined by using the collection of all sets as objects (aka small sets). The category of groups $\\mathbf{Grp}$ uses the collection of all groups (aka small groups). We can also construct the category $\\mathbf{Cat}$ of small categories, etc. All these are locally small.',
-	'If $\\mathcal{C}, \\mathcal{D}$ are two categories, we can construct the functor category $[\\mathcal{C}, \\mathcal{D}]$ as usual (there is simply no set-theoretic issue since collections behave just like sets). If $\\mathcal{C}$ is small and $\\mathcal{D}$ is locally small, then $[\\mathcal{C}, \\mathcal{D}]$ is locally small. This extra assumption on $\\mathcal{C}$ is one of many indicators why categories should not be assumed to be locally small by default. We could not even talk about the category of endofunctors of a general locally small category, so there would certainly be no category of monads. It is better to explicitly say when we need the assumption of being locally small.',
-	'The collections form a hypercategory $\\mathbf{Set}^+$. Likewise, we have a hypercategory $\\mathbf{Cat}^+$ consisting of all categories. For instance, $\\mathbf{Set}$ is an object of $\\mathbf{Cat}^+$, but not of  $\\mathbf{Cat}$. In our framework, we have no way to group all hypercollections (or even all hypercategories) into a single mathematical object; for this we would need a third Grothendieck universe, but usually this grouping is not required anyway.',
-	'If $\\mathcal{C}$ is any category and $A \\in \\mathcal{C}$ is an object, we have the Hom-functor $\\mathrm{Hom}(A,-) : \\mathcal{C} \\to \\mathbf{Set}^+$ defined as usual, but notice that it takes values in the hypercategory of all collections. The Yoneda Lemma and all of its corollaries can be proven as usual without ever assuming that $\\mathcal{C}$ is locally small. But if that happens to be the case, we get $\\mathrm{Hom}(A,-) : \\mathcal{C} \\to \\mathbf{Set}$, the target being a category.',
-	'We may define <i>adjunctions</i> as usual: we require natual isomorphisms $\\mathrm{Hom}(F(A),B) \\cong \\mathrm{Hom}(A,G(B))$ of functors valued in $\\mathbf{Set}^+$. We do not need to assume the categories to be locally small.',
-	'If $A$ is an object, the collection of all monomorphisms $B \\to A$ does not need to be a set. But if (for every choice of $A$) there is a set of such monomorphisms such that every monomorphism $B \\to A$ is isomorphic over $A$ to one in the set, then the category is called <i>well-powered</i>. The dual notion of being <i>well-copowered</i> is defined in the same way by using epimorphisms $A \\to B$. Every small category is well-powered, but there are many well-powered categories that are not small.',
-	'There is a lot more to say about the set-theoretic foundations of category theory (in fact, many papers have been written on the subject, and the approach developed above is just <i>one</i> of <a href="https://xkcd.com/927/" target="_blank">many</a> approaches), but this should be sufficient for the purposes of <i>CatDat</i>.',
-]
-
-export const load = () => {
-	return render_nested_formulas({ foundations })
+export const load = async () => {
+	const content = get_rendered_content('foundations')
+	return { content }
 }
diff --git a/src/routes/foundations/+page.svelte b/src/routes/foundations/+page.svelte
index 11d0880b..ffb17333 100644
--- a/src/routes/foundations/+page.svelte
+++ b/src/routes/foundations/+page.svelte
@@ -8,8 +8,4 @@
 	description="How to make sense of categories in set theory"
 />
 
-<h2>Foundations</h2>
-
-{#each data.foundations as para}
-	<p>{@html para}</p>
-{/each}
+{@html data.content}

From 7260341f2c649c221ecb045512b87f3e0d09a4b7 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 14 Apr 2026 20:18:41 +0200
Subject: [PATCH 6/7] improve foundations

---
 .vscode/settings.json          |  1 +
 src/lib/content/foundations.md | 63 ++++++++++++++++++++++++++++------
 2 files changed, 53 insertions(+), 11 deletions(-)

diff --git a/.vscode/settings.json b/.vscode/settings.json
index f8d45339..aa6cb7a7 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -143,6 +143,7 @@
 		"monomorphisms",
 		"morphism",
 		"morphisms",
+		"naturality",
 		"Niefield",
 		"nilradical",
 		"nlab",
diff --git a/src/lib/content/foundations.md b/src/lib/content/foundations.md
index ff158664..a674d34e 100644
--- a/src/lib/content/foundations.md
+++ b/src/lib/content/foundations.md
@@ -2,30 +2,71 @@
 
 In _CatDat_, we work with the following convenient set-theoretic foundation for category theory.
 
-We work with ZFC and two Grothendieck universes $U \in U^+$. So in principle everything is a set, but we will rename them as follows to introduce three levels of size: the sets in $U$ are renamed to _sets_ (sometimes for clarity: _small sets_), the sets in $U^+$ are renamed to _collections_ (sometimes also called _large sets_), and all sets are renamed to _hypercollections_ (which may or may not lie in $U^+$).
+### Sets, collections, and hypercollections
+
+We work with [ZFC](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory) and two [Grothendieck universes](https://en.wikipedia.org/wiki/Grothendieck_universe) $U \in U^+$. So in principle everything is a set, but we will rename them as follows to introduce three "levels of size":
+
+- The sets in $U$ are renamed to _sets_ (sometimes for clarity: _small sets_).
+- The sets in $U^+$ are renamed to _collections_ (sometimes also called _large sets_).
+- All available sets are renamed to _hypercollections_ (which may or may not lie in $U^+$).
 
 For example, $\mathbb{R}$ is a set, $U$ is a collection, and $U^+$ is a hypercollection. The collection $U$ consists of all sets, and the hypercollection $U^+$ consists of all collections. Every set is also a collection, and every collection is also a hypercollection.
 
-Note that sets, collections, and hypercollections all satisfy the ZFC axioms. In this sense, (hyper-)collections behave in the same way as sets. This is crucial for category theory. For example, we can form the collection of all maps between two collections. Just imagine three levels of ZFC on top of each other. Grothendieck universes are just an implementation detail, which we can _and will_ drop from now on. Sets are on level 1, collections on level 2, and hypercollections on level 3. You can imagine concrete mathematical objects like numbers or functions as being on level 0 (even though they are usually modeled as sets in ZFC).
+Note that sets, collections, and hypercollections all satisfy the ZFC axioms. In this sense, (hyper-)collections behave in the same way as sets. This is crucial for category theory. For example, we can form the collection of all maps between two collections. This basic property is not satisfied by [classes](<https://en.wikipedia.org/wiki/Class_(set_theory)>), which are not adequate for category theory.
+
+Just imagine three copies of ZFC included into each other, each representing a "level of size". Grothendieck universes are just an implementation detail, which we can _and will_ drop from now on. Sets are on level 1, collections on level 2, and hypercollections on level 3. You can imagine concrete mathematical objects like numbers or functions as being on level 0 (even though they are usually modeled as sets in ZFC).
+
+The levels are not defined by cardinality alone, though. For example, $\\{ U \\}$ is a collection which has just one element, but it is not a set (since otherwise $U$ would be a set). In particular, not every finite collection is a set. But of course, every finite collection is isomorphic to (has a bijection to) a set.
+
+In our framework, we have no way to group all hypercollections into a single mathematical object; for this we would need a third Grothendieck universe, but usually this grouping is not required anyway.
+
+### Categories
+
+A _category_ $\mathcal{C}$ has a pair of collections $O,M$, whose elements are called _objects_ resp. _morphisms_, as well as maps
+
+- $i : O \to M$ (_identity_),
+- $s : M \to O$ (_source_),
+- $t : M \to O$ (_target_),
+- $c : M \times_O M \to M$ (_composition_),
+
+such that the usual [axioms of a category](<https://en.wikipedia.org/wiki/Category_(mathematics)>) are satisfied. The domain of $c$ consists of all pairs of morphisms $(f,g)$ with $s(f)=t(g)$, and we always write $f \circ g := c(f,g)$ for their composition. Instead of $i(X)$ one usually writes $\mathrm{id}_X$ for the identity morphism of $X$. Formally, a category is a tuple
 
-A _category_ $\mathcal{C}$ is defined as a pair of collections $O,M$, whose elements are called _objects_ resp. _morphisms_, together with maps $i : O \to M$ (_identity_), $s : M \to O$ (_source_), $t : M \to O$ (_target_) as well as $c : M \times_O M \to M$ (_composition_), and the usual category axioms need to be satisfied. The domain of $c$ consists of all pairs of morphisms $(f,g)$ with $s(f)=t(g)$, and we always write $f \circ g := c(f,g)$ for their composition. Instead of $i(X)$ one usually writes $\mathrm{id}_X$ for the identity morphism of $X$.
+$\mathcal{C} = (O,M,i,s,t,c)$
 
-When $X \in O$ is an object, it is common to write $X \in \mathcal{C}$. When $f \in M$ is a morphism and $s(f) = X$, $t(f) = Y$, we write $f : X \to Y$. We write $\mathrm{Hom}(X,Y)$ for the collection of such morphisms with source $X$ and target $Y$. It is not necessarily a set. If this collection is a set for all $X,Y$, the category is called _locally small_.
+of collections (and hence a collection itself). We write $\mathrm{Ob}(\mathcal{C}) := O$ and $\mathrm{Mor}(\mathcal{C}) := M$. Instead of $X \in \mathrm{Ob}(\mathcal{C})$ we often write $X \in \mathcal{C}$.
+
+When $f \in \mathrm{Mor}(\mathcal{C})$ is a morphism and $s(f) = X$, $t(f) = Y$, we write $f : X \to Y$. We write $\mathrm{Hom}(X,Y)$ or $\mathrm{Mor}(X,Y)$ for the collection of such morphisms with source $X$ and target $Y$. It is not necessarily a set. If this collection is a set for all $X,Y$, the category is called _locally small_.
 
 A _small category_ is defined as above, just by using _sets_ $O$ and $M$ (instead of collections). A _hypercategory_ is also defined in the same way, but by using _hypercollections_ $O$ and $M$ (instead of collections). Every small category is also a category, and every category is also a hypercategory.
 
-Functors $\mathcal{C} \to \mathcal{C}'$ between all types of categories are defined as in every textbook on category theory; they are given by two maps $O \to O'$, $M \to M'$, etc. Between two categories there is a collection of all functors, in the same way that between two small categories there is a set of all functors.
+For example, the category of sets $\mathbf{Set}$ is defined by using the collection of all sets as objects (aka small sets). The category of groups $\mathbf{Grp}$ uses the collection of all groups (aka small groups). Other typical categories (topological spaces, graphs, metric spaces, etc.) can be constructed as usual. All these examples are locally small. Collections are the objects of a hypercategory $\mathbf{Set}^+$.
+
+### Functors
+
+A _functor_ $F : \mathcal{C} \to \mathcal{D}$ between between two categories (or small categories, or hypercategories) is defined as in every textbook on category theory; it consists of two maps $\mathrm{Ob}(F) : \mathrm{Ob}(\mathcal{C}) \to \mathrm{Ob}(\mathcal{D})$ and $\mathrm{Mor}(F) : \mathrm{Mor}(\mathcal{C}) \to \mathrm{Mor}(\mathcal{D})$ satisfying the [functor axioms](https://en.wikipedia.org/wiki/Functor). Between two categories there is a collection of all functors, in the same way that between two small categories there is a set of all functors.
+
+Small categories and functors form the category $\mathbf{Cat}$ of small categories, which is locally small. There is also a hypercategory $\mathbf{Cat}^+$ consisting of all categories. For instance, $\mathbf{Set}$ is an object of $\mathbf{Cat}^+$, but not of $\mathbf{Cat}$.
+
+If $F,G : \mathcal{C} \rightrightarrows \mathcal{D}$ are two functors, a morphism $F \to G$ (or _natural transformation_) is defined as a map $\mathrm{Ob}(\mathcal{C}) \to \mathrm{Mor}(\mathcal{D})$ as usual satisfying the naturality condition. These morphisms form a collection $\mathrm{Hom}(F,G)$.
+
+If $\mathcal{C}, \mathcal{D}$ are two categories, we can now construct the functor category $[\mathcal{C}, \mathcal{D}]$ as usual. There is simply no set-theoretic issue since collections behave just like sets. If $\mathcal{C}$ is small and $\mathcal{D}$ is locally small, then $[\mathcal{C}, \mathcal{D}]$ is locally small. This extra assumption on $\mathcal{C}$ is one of many indicators why categories should not be assumed to be locally small by default. We could not even talk about the category of endofunctors of a general category if everything needs to be locally small, so there would certainly be no category of monads.
+
+It is better to explicitly say when we need the assumption of being locally small.
+
+### Representable Functors
+
+If $\mathcal{C}$ is any category and $A \in \mathcal{C}$ is an object, we have the Hom-functor
 
-The category of sets $\mathbf{Set}$ is defined by using the collection of all sets as objects (aka small sets). The category of groups $\mathbf{Grp}$ uses the collection of all groups (aka small groups). We can also construct the category $\mathbf{Cat}$ of small categories, etc. All these are locally small.
+$\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}^+$
 
-If $\mathcal{C}, \mathcal{D}$ are two categories, we can construct the functor category $[\mathcal{C}, \mathcal{D}]$ as usual (there is simply no set-theoretic issue since collections behave just like sets). If $\mathcal{C}$ is small and $\mathcal{D}$ is locally small, then $[\mathcal{C}, \mathcal{D}]$ is locally small. This extra assumption on $\mathcal{C}$ is one of many indicators why categories should not be assumed to be locally small by default. We could not even talk about the category of endofunctors of a general locally small category, so there would certainly be no category of monads. It is better to explicitly say when we need the assumption of being locally small.
+defined as usual, but notice that it takes values in the hypercategory of all collections. The Yoneda Lemma and all of its corollaries can be proven as usual without ever assuming that $\mathcal{C}$ is locally small. But if that happens to be the case, we get $\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}$, the target being a category.
 
-The collections form a hypercategory $\mathbf{Set}^+$. Likewise, we have a hypercategory $\mathbf{Cat}^+$ consisting of all categories. For instance, $\mathbf{Set}$ is an object of $\mathbf{Cat}^+$, but not of $\mathbf{Cat}$. In our framework, we have no way to group all hypercollections (or even all hypercategories) into a single mathematical object; for this we would need a third Grothendieck universe, but usually this grouping is not required anyway.
+We may define _adjunctions_ as usual: we require natural isomorphisms $\mathrm{Hom}(F(A),B) \cong \mathrm{Hom}(A,G(B))$ of functors valued in $\mathbf{Set}^+$. We do not need to assume the categories to be locally small. They can also be defined by morphisms of functors $\mathrm{id} \to G \circ F$ and $F \circ G \to \mathrm{id}$ satisfying the triangle identities.
 
-If $\mathcal{C}$ is any category and $A \in \mathcal{C}$ is an object, we have the Hom-functor $\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}^+$ defined as usual, but notice that it takes values in the hypercategory of all collections. The Yoneda Lemma and all of its corollaries can be proven as usual without ever assuming that $\mathcal{C}$ is locally small. But if that happens to be the case, we get $\mathrm{Hom}(A,-) : \mathcal{C} \to \mathbf{Set}$, the target being a category.
+### Well-powered categories
 
-We may define _adjunctions_ as usual: we require natural isomorphisms $\mathrm{Hom}(F(A),B) \cong \mathrm{Hom}(A,G(B))$ of functors valued in $\mathbf{Set}^+$. We do not need to assume the categories to be locally small.
+If $A$ is an object of a category, the collection of all monomorphisms $B \to A$ does not need to be a set. But if (for every choice of $A$) there is a set of such monomorphisms such that every monomorphism $B \to A$ is isomorphic over $A$ to one in the set, then the category is called _well-powered_. The dual notion of being _well-copowered_ is defined in the same way by using epimorphisms $A \to B$. Every small category is well-powered, but there are many well-powered categories that are not small, not even equivalent to a small category.
 
-If $A$ is an object, the collection of all monomorphisms $B \to A$ does not need to be a set. But if (for every choice of $A$) there is a set of such monomorphisms such that every monomorphism $B \to A$ is isomorphic over $A$ to one in the set, then the category is called _well-powered_. The dual notion of being _well-copowered_ is defined in the same way by using epimorphisms $A \to B$. Every small category is well-powered, but there are many well-powered categories that are not small.
+### Conclusion
 
 There is a lot more to say about the set-theoretic foundations of category theory (in fact, many papers have been written on the subject, and the approach developed above is just _one_ of [many](https://xkcd.com/927/) approaches), but this should be sufficient for the purposes of _CatDat_.

From 8b5477fd84070defd65a0167b4935101fdc0b857 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 15 Apr 2026 09:25:32 +0200
Subject: [PATCH 7/7] collapse suggestion form by default, open it via button

---
 src/components/SuggestionForm.svelte | 160 +++++++++++++++------------
 1 file changed, 88 insertions(+), 72 deletions(-)

diff --git a/src/components/SuggestionForm.svelte b/src/components/SuggestionForm.svelte
index ba11e9c7..8eccee6a 100644
--- a/src/components/SuggestionForm.svelte
+++ b/src/components/SuggestionForm.svelte
@@ -61,88 +61,104 @@
 	}
 
 	let section = $state<HTMLElement | null>(null)
+
+	let hide_form = $state(true)
+
+	async function show_form() {
+		hide_form = false
+		await tick()
+		section?.scrollIntoView({
+			block: 'start',
+			behavior: 'smooth',
+		})
+	}
 </script>
 
 <section bind:this={section}>
-	<h2>Suggestion Form</h2>
-
-	<p class="hint">
-		Use the form below to report missing data, submit an issue, or make a suggestion.
-	</p>
-
-	<form onsubmit={create_issue}>
-		<div class="form-group">
-			<label for="title">
-				<span>Short summary</span>
-				<span class="description">max. {TITLE_MAX_LENGTH} characters</span>
-			</label>
-			<input
-				type="text"
-				id="title"
-				class="full-width"
-				bind:value={title}
-				required
-				aria-invalid={title.length > TITLE_MAX_LENGTH}
-			/>
-		</div>
-
-		<div class="form-group">
-			<label for="body">
-				<span>Details</span>
-				<span class="description">max. {BODY_MAX_LENGTH} characters</span>
-			</label>
-			<textarea
-				id="body"
-				{@attach resize_textarea}
-				bind:value={body}
-				required
-				class="full-width"
-				aria-invalid={body.length > BODY_MAX_LENGTH}
-			></textarea>
-		</div>
-
-		<div class="form-group">
-			<label for="name">
-				<span>Your name</span>
-				<span class="description">optional</span>
-			</label>
-			<input
-				type="text"
-				id="name"
-				class="full-width"
-				bind:value={name}
-				aria-invalid={name.length > NAME_MAX_LENGTH}
-			/>
-		</div>
-
-		<button class="button" disabled={sending}>
-			{#if sending}
-				Submitting...
-			{:else}
-				Submit
-			{/if}
-		</button>
-	</form>
-
-	{#if error}
-		<p class="error">
-			<Fa icon={faWarning} />
-			Error: {error}
+	{#if hide_form}
+		<button class="button" onclick={show_form}>Make a suggestion</button>
+	{:else}
+		<h2>Suggestion Form</h2>
+
+		<p class="hint">
+			Use the form below to report missing data, submit an issue, or make a
+			suggestion.
 		</p>
-	{/if}
 
-	{#if url}
-		<p>
-			<Fa icon={faCheckCircle} />
-			Your suggestion has been created as a
-			<a href={url} target="_blank">GitHub issue</a>. We will review it shortly.
-		</p>
+		<form onsubmit={create_issue}>
+			<div class="form-group">
+				<label for="title">
+					<span>Short summary</span>
+					<span class="description">max. {TITLE_MAX_LENGTH} characters</span>
+				</label>
+				<input
+					type="text"
+					id="title"
+					class="full-width"
+					bind:value={title}
+					required
+					aria-invalid={title.length > TITLE_MAX_LENGTH}
+				/>
+			</div>
+
+			<div class="form-group">
+				<label for="body">
+					<span>Details</span>
+					<span class="description">max. {BODY_MAX_LENGTH} characters</span>
+				</label>
+				<textarea
+					id="body"
+					{@attach resize_textarea}
+					bind:value={body}
+					required
+					class="full-width"
+					aria-invalid={body.length > BODY_MAX_LENGTH}
+				></textarea>
+			</div>
+
+			<div class="form-group">
+				<label for="name">
+					<span>Your name</span>
+					<span class="description">optional</span>
+				</label>
+				<input
+					type="text"
+					id="name"
+					class="full-width"
+					bind:value={name}
+					aria-invalid={name.length > NAME_MAX_LENGTH}
+				/>
+			</div>
+
+			<button class="button" disabled={sending}>
+				{#if sending}
+					Submitting...
+				{:else}
+					Submit
+				{/if}
+			</button>
+		</form>
+
+		{#if error}
+			<p class="error">
+				<Fa icon={faWarning} />
+				Error: {error}
+			</p>
+		{/if}
+
+		{#if url}
+			<p>
+				<Fa icon={faCheckCircle} />
+				Your suggestion has been created as a
+				<a href={url} target="_blank">GitHub issue</a>. We will review it shortly.
+			</p>
+		{/if}
 	{/if}
 </section>
 
 <style>
 	section {
-		margin-top: 4rem;
+		margin-top: 2rem;
 		padding-bottom: 1rem;
 		margin-bottom: -1rem;
 	}