Adjust hyphenation

Author: ykawase5048

database/data/003_properties/002_limits-colimits-existence.sql

@@ -328,34 +328,34 @@ VALUES
 	TRUE
 ),
 (
-	'multilimits',
+	'multi-limits',
 	'has',
-	'This property refers to the existence of multilimits of small diagrams. Note that any diagram with no cone admits a multilimit, which is the empty set of cones.',
+	'This property refers to the existence of multi-limits of small diagrams. Note that any diagram with no cone admits a multi-limit, which is the empty set of cones.',
 	'https://ncatlab.org/nlab/show/multilimit',
-	'multicolimits',
+	'multi-colimits',
 	TRUE
 ),
 (
-	'multicolimits',
+	'multi-colimits',
 	'has',
-	'This property refers to the existence of multicolimits of small diagrams. Note that any diagram with no cocone admits a multicolimit, which is the empty set of cocones.',
+	'This property refers to the existence of multi-colimits of small diagrams. Note that any diagram with no cocone admits a multi-colimit, which is the empty set of cocones.',
 	'https://ncatlab.org/nlab/show/multilimit',
-	'multilimits',
+	'multi-limits',
 	TRUE
 ),
 (
-	'multiterminal object',
+	'multi-terminal object',
 	'has a',
-	'This property refers to the existence of a multilimit of the empty diagram. A category has a multiterminal object if and only if each connected component has a terminal object.',
+	'This property refers to the existence of a multi-limit of the empty diagram. A category has a multi-terminal object if and only if each connected component has a terminal object.',
 	'https://ncatlab.org/nlab/show/multilimit',
-	'multiinitial object',
+	'multi-initial object',
 	TRUE
 ),
 (
-	'multiinitial object',
+	'multi-initial object',
 	'has a',
-	'This property refers to the existence of a multicolimit of the empty diagram. A category has a multiinitial object if and only if each connected component has a initial object.',
+	'This property refers to the existence of a multi-colimit of the empty diagram. A category has a multi-initial object if and only if each connected component has a initial object.',
 	'https://ncatlab.org/nlab/show/multilimit',
-	'multiterminal object',
+	'multi-terminal object',
 	TRUE
 );

database/data/003_properties/008_locally-presentable.sql

@@ -96,33 +96,33 @@ VALUES
 	TRUE
 ),
 (
-	'multialgebraic',
+	'multi-algebraic',
 	'is',
-	'A category is <i>multialgebraic</i> if it is equivalent to the category of models of an FPC-sketch, where FPC represents finite products and small coproducts. This notion was introduced by <a href="https://doi.org/10.1007/BF01224953" target="_blank">Diers</a>.',
+	'A category is <i>multi-algebraic</i> if it is equivalent to the category of models of an FPC-sketch, where FPC represents finite products and small coproducts. This notion was introduced by <a href="https://doi.org/10.1007/BF01224953" target="_blank">Diers</a>.',
 	NULL,
 	NULL,
 	TRUE
 ),
 (
-	'locally multipresentable',
+	'locally multi-presentable',
 	'is',
-	'Let $\kappa$ be a regular cardinal. A category is <i>locally $\kappa$-multipresentable</i> if it is $\kappa$-accessible and has connected limits. It is known that a category is locally $\kappa$-multipresentable if and only if it is equivalent to the category of models of a limit-coproduct sketch; see Thm. 4.32 in <a href="https://ncatlab.org/nlab/show/Locally+Presentable+and+Accessible+Categories" target="_blank">Adamek-Rosicky</a> and the remark below. A category is called <i>locally multipresentable</i> if it is locally $\kappa$-multipresentable for some $\kappa$, equivalently, it is accessible and has connected limits.',
+	'Let $\kappa$ be a regular cardinal. A category is <i>locally $\kappa$-multi-presentable</i> if it is $\kappa$-accessible and has connected limits. It is known that a category is locally $\kappa$-multi-presentable if and only if it is equivalent to the category of models of a limit-coproduct sketch; see Thm. 4.32 in <a href="https://ncatlab.org/nlab/show/Locally+Presentable+and+Accessible+Categories" target="_blank">Adamek-Rosicky</a> and the remark below. A category is called <i>locally multi-presentable</i> if it is locally $\kappa$-multi-presentable for some $\kappa$, equivalently, it is accessible and has connected limits.',
 	'https://ncatlab.org/nlab/show/locally+multipresentable+category',
 	NULL,
 	TRUE
 ),
 (
-	'locally finitely multipresentable',
+	'locally finitely multi-presentable',
 	'is',
-	'A category is <i>locally finitely multipresentable</i> if it is finitely accessible and has connected limits.',
+	'A category is <i>locally finitely multi-presentable</i> if it is finitely accessible and has connected limits.',
 	'https://ncatlab.org/nlab/show/locally+multipresentable+category',
 	NULL,
 	TRUE
 ),
 (
-	'locally polypresentable',
+	'locally poly-presentable',
 	'is',
-	'A category is <i>locally polypresentable</i> if it is accessible and has wide pullbacks.',
+	'A category is <i>locally poly-presentable</i> if it is accessible and has wide pullbacks.',
 	'https://ncatlab.org/nlab/show/locally+polypresentable+category',
 	NULL,
 	TRUE

database/data/004_property-assignments/0.sql

@@ -31,7 +31,7 @@ VALUES
 ),
 (
 	'0',
-	'multialgebraic',
+	'multi-algebraic',
 	TRUE,
 	'The terminal category $\mathbf{1}$ becomes an FPC-sketch by selecting the unique empty cone and cocone. Then, a $\mathbf{Set}$-valued model of this sketch is a functor $\mathbf{1} \to \mathbf{Set}$ sending the unique object to a terminal and initial object, which never exists. Hence, $\mathbf{0}$ is the category of models of this FPC-sketch.'
 ),

database/data/004_property-assignments/2.sql

@@ -25,7 +25,7 @@ VALUES
 ),
 (
 	'2',
-	'multialgebraic',
+	'multi-algebraic',
 	TRUE,
 	'There is an FPC-sketch whose $\mathbf{Set}$-model is precisely a pair $(X,Y)$ of sets such that the coproduct $X+Y$ is a singleton. Any $\mathbf{Set}$-model of such a sketch is isomorphic to either $(\varnothing, 1)$ or $(1, \varnothing)$, hence the category of models is equivalent to $\mathbf{2}$.'
 ),

database/data/004_property-assignments/B.sql

@@ -61,7 +61,7 @@ VALUES
 ),
 (
 	'B',
-	'multiterminal object',
+	'multi-terminal object',
 	FALSE,
 	'This is trivial.'
 ),

database/data/004_property-assignments/FS.sql

@@ -55,9 +55,9 @@ VALUES
 ),
 (
 	'FS',
-	'multiterminal object',
+	'multi-terminal object',
 	TRUE,
-	'The empty set and a singleton give a multiterminal object.'
+	'The empty set and a singleton give a multi-terminal object.'
 ),
 (
 	'FS',
@@ -125,7 +125,7 @@ VALUES
 ),
 (
 	'FS',
-	'multiinitial object',
+	'multi-initial object',
 	FALSE,
 	'This is trivial.'
 ),

database/data/004_property-assignments/Fld.sql

@@ -31,7 +31,7 @@ VALUES
 ),
 (
 	'Fld',
-	'multialgebraic',
+	'multi-algebraic',
 	TRUE,
 	'See Eg. 4.3(1) in <a href="http://www.tac.mta.ca/tac/volumes/8/n3/8-03abs.html" target="_blank">[AR01]</a>.'
 ),
@@ -91,7 +91,7 @@ VALUES
 ),
 (
 	'Fld',
-	'multiterminal object',
+	'multi-terminal object',
 	FALSE,
-	'Every field has a non-trivial extension, for instance, the rational function field over itself in one variable. Hence, a multiterminal object never exists.'
+	'Every field has a non-trivial extension, for instance, the rational function field over itself in one variable. Hence, a multi-terminal object never exists.'
 );

database/data/004_property-assignments/Setne.sql

@@ -97,9 +97,9 @@ VALUES
 ),
 (
 	'Setne',
-	'multilimits',
+	'multi-limits',
 	TRUE,
-	'Let $D$ be a diagram in $\mathbf{Set}_{\neq \varnothing}$, and let $L$ be a limit of $D$ in $\mathbf{Set}$. If $L$ is non-empty, it gives a limit in $\mathbf{Set}_{\neq \varnothing}$ as well. If $L$ is the empty set, there is no cone over $D$ in $\mathbf{Set}_{\neq \varnothing}$; hence the empty set of cone gives a multilimit of $D$ in $\mathbf{Set}_{\neq \varnothing}$.'
+	'Let $D$ be a diagram in $\mathbf{Set}_{\neq \varnothing}$, and let $L$ be a limit of $D$ in $\mathbf{Set}$. If $L$ is non-empty, it gives a limit in $\mathbf{Set}_{\neq \varnothing}$ as well. If $L$ is the empty set, there is no cone over $D$ in $\mathbf{Set}_{\neq \varnothing}$; hence the empty set of cone gives a multi-limit of $D$ in $\mathbf{Set}_{\neq \varnothing}$.'
 ),
 (
 	'Setne',

database/data/005_implications/001_limits-colimits-existence-implications.sql

@@ -273,23 +273,23 @@ VALUES
 	FALSE
 ),
 (
-	'multilimits_generalize_limits',
+	'multi-limits_generalize_limits',
 	'["complete"]',
-	'["multilimits"]',
-	'Limits are precisely multilimits such that the set of cones is singleton.',
+	'["multi-limits"]',
+	'Limits are precisely multi-limits such that the set of cones is singleton.',
 	FALSE
 ),
 (
-	'multiterminal_special_case',
-	'["multilimits"]',
-	'["multiterminal object"]',
+	'multi-terminal_special_case',
+	'["multi-limits"]',
+	'["multi-terminal object"]',
 	'This is trivial.',
 	FALSE
 ),
 (
-	'multiterminal_with_connected',
-	'["connected","multiterminal object"]',
+	'multi-terminal_with_connected',
+	'["connected","multi-terminal object"]',
 	'["terminal object"]',
-	'Let $(T_i)_{i\in I}$ be a multiterminal object in a connected category $\mathcal{C}$. By definition of multiterminal objects, for each object $C$, there are a unique index $i_C\in I$ and a unique morphism $C \to T_{i_C}$. Since the index $i_C$ is invariant under connected components, $I$ must be a singleton. The converse is trivial.',
+	'Let $(T_i)_{i\in I}$ be a multi-terminal object in a connected category $\mathcal{C}$. By definition of multi-terminal objects, for each object $C$, there are a unique index $i_C\in I$ and a unique morphism $C \to T_{i_C}$. Since the index $i_C$ is invariant under connected components, $I$ must be a singleton. The converse is trivial.',
 	TRUE
 );

database/data/005_implications/007_locally-presentable-implications.sql

@@ -161,58 +161,58 @@ VALUES
 	FALSE
 ),
 (
-	'locally_multipresentable_definition',
-	'["locally multipresentable"]',
+	'locally_multi-presentable_definition',
+	'["locally multi-presentable"]',
 	'["accessible", "connected limits"]',
 	'This is trivial.',
 	TRUE
 ),
 (
-	'locally_multipresentable_another_definition',
-	'["locally multipresentable"]',
-	'["accessible", "multicolimits"]',
+	'locally_multi-presentable_another_definition',
+	'["locally multi-presentable"]',
+	'["accessible", "multi-colimits"]',
 	'See <a href="https://ncatlab.org/nlab/show/Locally+Presentable+and+Accessible+Categories" target="_blank">Adamek-Rosicky</a>, 4.30.',
 	TRUE
 ),
 (
-	'locally_finitely_multipresentable_definition',
-	'["locally finitely multipresentable"]',
+	'locally_finitely_multi-presentable_definition',
+	'["locally finitely multi-presentable"]',
 	'["finitely accessible", "connected limits"]',
 	'This is trivial.',
 	TRUE
 ),
 (
-	'locally_finitely_multipresentable_another_definition',
-	'["locally finitely multipresentable"]',
-	'["finitely accessible", "multicolimits"]',
+	'locally_finitely_multi-presentable_another_definition',
+	'["locally finitely multi-presentable"]',
+	'["finitely accessible", "multi-colimits"]',
 	'See <a href="https://ncatlab.org/nlab/show/Locally+Presentable+and+Accessible+Categories" target="_blank">Adamek-Rosicky</a>, 4.30.',
 	TRUE
 ),
 (
-	'locally_polypresentable_definition',
-	'["locally polypresentable"]',
+	'locally_poly-presentable_definition',
+	'["locally poly-presentable"]',
 	'["accessible", "wide pullbacks"]',
 	'This is trivial.',
 	TRUE
 ),
 (
-	'multialgebraic_implies_locally_finitely_multipresentable',
-	'["multialgebraic"]',
-	'["locally finitely multipresentable"]',
-	'This follows from the fact that a category is locally finitely multipresentable if and only if it is equivalent to the category of models of an FLC-sketch, where FLC represents finite limits and small coproducts.',
+	'multi-algebraic_implies_locally_finitely_multi-presentable',
+	'["multi-algebraic"]',
+	'["locally finitely multi-presentable"]',
+	'This follows from the fact that a category is locally finitely multi-presentable if and only if it is equivalent to the category of models of an FLC-sketch, where FLC represents finite limits and small coproducts.',
 	FALSE
 ),
 (
-	'varieties_are_multialgebraic',
+	'varieties_are_multi-algebraic',
 	'["locally strongly finitely presentable"]',
-	'["multialgebraic"]',
+	'["multi-algebraic"]',
 	'This is because that every FP-sketch is an FPC-sketch.',
 	FALSE
 ),
 (
-	'multialgebraic_another_definition',
-	'["multialgebraic"]',
-	'["generalized variety", "multicolimits"]',
+	'multi-algebraic_another_definition',
+	'["multi-algebraic"]',
+	'["generalized variety", "multi-colimits"]',
 	'See <a href="http://www.tac.mta.ca/tac/volumes/8/n3/8-03abs.html" target="_blank">[AR01, Thm. 4.4]</a>.',
 	TRUE
 );