Turn FiberProductEmbeddingOfDirect(Product/Sum) into a GAP function

Also for the duals

Author: Tom Kuhmichel

CAP/gap/UniversalObjects.gd

@@ -1762,6 +1762,14 @@ DeclareOperation( "IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct"
 #! @Description
 #! The argument is a list of morphisms $D = ( \beta_i: P_i \rightarrow B )_{i = 1 \dots n}$.
 #! The output is the natural embedding
+#! $\mathrm{FiberProduct}(D) \rightarrow \prod_{i=1}^n P_i$.
+#! @Returns a morphism in $\mathrm{Hom}( \mathrm{FiberProduct}(D), \prod_{i=1}^n P_i )$
+#! @Arguments D
+DeclareOperation( "FiberProductEmbeddingInDirectProduct",
+                  [ IsList ] );
+#! @Description
+#! The argument is a list of morphisms $D = ( \beta_i: P_i \rightarrow B )_{i = 1 \dots n}$.
+#! The output is the natural embedding
 #! $\mathrm{FiberProduct}(D) \rightarrow \bigoplus_{i=1}^n P_i$.
 #! @Returns a morphism in $\mathrm{Hom}( \mathrm{FiberProduct}(D), \bigoplus_{i=1}^n P_i )$
 #! @Arguments D
@@ -1958,13 +1966,22 @@ DeclareOperation( "IsomorphismFromPushoutToCoequalizerOfCoproductDiagram",
 DeclareOperation( "IsomorphismFromCoequalizerOfCoproductDiagramToPushout",
                   [ IsList ] );
 
+#! @Description
+#! The argument is a list of morphisms $D = ( \beta_i: B \rightarrow I_i )_{i = 1 \dots n}$.
+#! The output is the natural projection
+#! $\bigsqcup_{i=1}^n I_i \rightarrow \mathrm{Pushout}(D)$.
+#! @Returns a morphism in $\mathrm{Hom}( \bigsqcup {i=1}^n I_i, \mathrm{Pushout}(D) )$
+#! @Arguments D
+DeclareOperation( "PushoutProjectionFromCoproduct",
+                  [ IsList ] );
+
 #! @Description
 #! The argument is a list of morphisms $D = ( \beta_i: B \rightarrow I_i )_{i = 1 \dots n}$.
 #! The output is the natural projection
 #! $\bigoplus_{i=1}^n I_i \rightarrow \mathrm{Pushout}(D)$.
 #! @Returns a morphism in $\mathrm{Hom}( \bigoplus_{i=1}^n I_i, \mathrm{Pushout}(D) )$
 #! @Arguments D
-DeclareOperation( "DirectSumProjectionInPushout",
+DeclareOperation( "PushoutProjectionFromDirectSum",
                   [ IsList ] );
 
 #! @Description

CAP/gap/UniversalObjects.gi

@@ -503,6 +503,56 @@ InstallGlobalFunction( FiberProduct,
 
 end );
 
+##
+InstallMethod( FiberProductEmbeddingInDirectProduct,
+        [ IsList ],
+        
+  function( diagram )
+    
+    return FiberProductEmbeddingInDirectProduct( CapCategory( diagram[1] ), diagram );
+    
+end );
+
+##
+InstallOtherMethod( FiberProductEmbeddingInDirectProduct,
+        [ IsCapCategory, IsList ],
+        
+  function( cat, diagram )
+    local sources_of_diagram, test_source;
+    
+    sources_of_diagram := List( diagram, Source );
+    
+    test_source := List( [ 1 .. Length( diagram ) ], i -> ProjectionInFactorOfFiberProduct( cat, diagram, i ) );
+    
+    return UniversalMorphismIntoDirectProduct( cat, sources_of_diagram, FiberProduct( cat, diagram ), test_source );
+    
+end );
+
+##
+InstallMethod( FiberProductEmbeddingInDirectSum,
+        [ IsList ],
+        
+  function( diagram )
+    
+    return FiberProductEmbeddingInDirectProduct( CapCategory( diagram[1] ), diagram );
+    
+end );
+
+##
+InstallOtherMethod( FiberProductEmbeddingInDirectSum,
+        [ IsCapCategory, IsList ],
+        
+  function( cat, diagram )
+    local sources_of_diagram, test_source;
+    
+    sources_of_diagram := List( diagram, Source );
+    
+    test_source := List( [ 1 .. Length( diagram ) ], i -> ProjectionInFactorOfFiberProduct( cat, diagram, i ) );
+    
+    return UniversalMorphismIntoDirectSum( cat, sources_of_diagram, FiberProduct( cat, diagram ), test_source );
+    
+end );
+
 ####################################
 ##
 ## Coequalizer
@@ -782,6 +832,56 @@ InstallMethod( Pushout,
 
 end );
 
+##
+InstallMethod( PushoutProjectionFromCoproduct,
+        [ IsList ],
+                    
+  function( diagram )
+    
+    return PushoutProjectionFromCoproduct( CapCategory( diagram[1] ), diagram );
+    
+end );
+
+##
+InstallOtherMethod( PushoutProjectionFromCoproduct,
+        [ IsCapCategory, IsList ],
+                    
+  function( cat, diagram )
+    local ranges_of_diagram, test_sink;
+    
+    ranges_of_diagram := List( diagram, Range );
+    
+    test_sink := List( [ 1 .. Length( diagram ) ], i -> InjectionOfCofactorOfPushout( cat, diagram, i ) );
+    
+    return UniversalMorphismFromCoproduct( cat, ranges_of_diagram, Pushout( cat, diagram ), test_sink );
+    
+end );
+
+##
+InstallMethod( PushoutProjectionFromDirectSum,
+        [ IsList ],
+                    
+  function( diagram )
+    
+    return PushoutProjectionFromDirectSum( CapCategory( diagram[1] ), diagram );
+    
+end );
+
+##
+InstallOtherMethod( PushoutProjectionFromDirectSum,
+        [ IsCapCategory, IsList ],
+                    
+  function( cat, diagram )
+    local ranges_of_diagram, test_sink;
+    
+    ranges_of_diagram := List( diagram, Range );
+    
+    test_sink := List( [ 1 .. Length( diagram ) ], i -> InjectionOfCofactorOfPushout( cat, diagram, i ) );
+    
+    return UniversalMorphismFromDirectSum( cat, ranges_of_diagram, Pushout( cat, diagram ), test_sink );
+    
+end );
+
 ####################################
 ##
 ## Coimage