relocated code

Author: mohamed-barakat

Toposes/doc/Doc.autodoc

@@ -20,10 +20,6 @@ variations are implemented in the CAP-based package `CartesianCategories`.
 
 @Section Heyting algebra of subobjects
 
-@Section Lawvere-Tierney topologies
-
-@InsertChunk LawvereTierney
-
 @Section Pushout complements
 
 @Subsection Example in FinSets
@@ -36,6 +32,10 @@ variations are implemented in the CAP-based package `CartesianCategories`.
 
 @Section Double-pushout rewriting
 
+@Section Lawvere-Tierney topologies
+
+@InsertChunk LawvereTierney
+
 @Section Add-methods
 
 @Chapter Category of relations

Toposes/gap/Topos.gd

@@ -546,6 +546,35 @@ DeclareOperation( "EmbeddingOfRelativePseudoComplementSubobject",
 DeclareOperation( "EmbeddingOfRelativePseudoComplementSubobjectWithGivenImplication",
         [ IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject ] );
 
+###################################
+##
+#! @Section Pushout complements
+##
+###################################
+
+#! @Description
+#!  The arguments are two composable morphisms $l: K \rightarrow L$, $m: L \rightarrow G$.
+#!  The output is <C>true</C> if there exists a morphism $d: K \rightarrow D$ and a morphism $g: D \rightarrow G$
+#!  such that the four morphisms $l,d,m,g$ form a pushout diagram, i.e., such that
+#!  $m$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 1) and
+#!  $g$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 2).
+#!  Otherwise the output is <C>false</C>.
+#! @Returns a boolean
+#! @Arguments l, m
+DeclareOperation( "HasPushoutComplement",
+        [ IsCapCategoryMorphism, IsCapCategoryMorphism ] );
+
+#! @Description
+#!  The arguments are two composable morphisms $l: K \rightarrow L$, $m: L \rightarrow G$.
+#!  The output is a morphism $d: K \rightarrow D$ such that there exists a morphism $g: D \rightarrow G$
+#!  turing the four morphisms $l,d,m,g$ into a pushout diagram, i.e., such that
+#!  $m$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 1) and
+#!  $g$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 2).
+#! @Returns a morphism
+#! @Arguments l, m
+DeclareOperation( "PushoutComplement",
+        [ IsCapCategoryMorphism, IsCapCategoryMorphism ] );
+
 ###################################
 ##
 #! @Section Lawvere-Tierney topologies
@@ -576,32 +605,3 @@ DeclareAttribute( "LawvereTierneySubobjects",
 #! @Arguments T
 DeclareAttribute( "LawvereTierneyEmbeddingsOfSubobjectClassifiers",
         IsCapCategory );
-
-###################################
-##
-#! @Section Pushout complements
-##
-###################################
-
-#! @Description
-#!  The arguments are two composable morphisms $l: K \rightarrow L$, $m: L \rightarrow G$.
-#!  The output is <C>true</C> if there exists a morphism $d: K \rightarrow D$ and a morphism $g: D \rightarrow G$
-#!  such that the four morphisms $l,d,m,g$ form a pushout diagram, i.e., such that
-#!  $m$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 1) and
-#!  $g$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 2).
-#!  Otherwise the output is <C>false</C>.
-#! @Returns a boolean
-#! @Arguments l, m
-DeclareOperation( "HasPushoutComplement",
-        [ IsCapCategoryMorphism, IsCapCategoryMorphism ] );
-
-#! @Description
-#!  The arguments are two composable morphisms $l: K \rightarrow L$, $m: L \rightarrow G$.
-#!  The output is a morphism $d: K \rightarrow D$ such that there exists a morphism $g: D \rightarrow G$
-#!  turing the four morphisms $l,d,m,g$ into a pushout diagram, i.e., such that
-#!  $m$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 1) and
-#!  $g$=<C>InjectionOfCofactorOfPushoutWithGivenPushout</C>([$l,d$], 2).
-#! @Returns a morphism
-#! @Arguments l, m
-DeclareOperation( "PushoutComplement",
-        [ IsCapCategoryMorphism, IsCapCategoryMorphism ] );