relocated code from Algebroids.g? -> CategoryOfAlgebroids.g?

Author: heiderich

PackageInfo.g

@@ -15,7 +15,7 @@ Version := Maximum( [
                    ## this line prevents merge conflicts
                    "2020.09-08", ## Kamal's version
                    ## this line prevents merge conflicts
-                   "2019.02-12", ## Florian's version
+                   "2020.10-02", ## Florian's version
                    ## this line prevents merge conflicts
                    "2019.10-30", ## Sepp's version
                    ] ),

gap/Algebroids.gd

@@ -31,35 +31,11 @@ DeclareCategory( "IsCapCategoryMorphismInAlgebroid",
 DeclareCategory( "IsAlgebroid",
         IsCapCategory );
 
-#! @Description
-#!  The ⪆ category of morphisms of algebroids.
-DeclareCategory( "IsAlgebroidMorphism",
-        IsCapFunctor );
-
 #! @Description
 #!  The ⪆ category of algebras.
 DeclareCategory( "IsAlgebraAsCategory",
         IsAlgebroid );
 
-#! @Description
-#! The GAP category of objects in the category
-#! of algebroids over a ring $R$.
-#! @Arguments object
-DeclareCategory( "IsCategoryOfAlgebroidsObject",
-                 IsCapCategoryObject );
-
-#! @Description
-#! The GAP category of morphisms in the category
-#! of algebroids over a ring $R$.
-#! @Arguments object
-DeclareCategory( "IsCategoryOfAlgebroidsMorphism",
-                 IsCapCategoryMorphism );
-
-DeclareGlobalFunction( "INSTALL_FUNCTIONS_FOR_CATEGORY_OF_ALGEBROIDS" );
-
-DeclareCategory( "IsCategoryOfAlgebroids",
-                 IsCapCategory );
-
 ####################################
 #
 #! @Section Properties
@@ -83,26 +59,20 @@ CAP_INTERNAL_CONSTRUCTIVE_CATEGORIES_RECORD.IsFinitelyPresentedCategory := Conca
 #! @Returns true or false
 DeclareProperty( "IsCommutative",
         IsAlgebroid );
-DeclareProperty( "IsCommutative",
-        IsCategoryOfAlgebroidsObject );
 
 #! @Description
 #!  Check whether <A>B</A> is counitary.
 #! @Arguments B
 #! @Returns true or false
 DeclareProperty( "IsCounitary",
         IsAlgebroid );
-DeclareProperty( "IsCounitary",
-        IsCategoryOfAlgebroidsObject );
 
 #! @Description
 #!  Check whether <A>B</A> is coassociative.
 #! @Arguments B
 #! @Returns true or false
 DeclareProperty( "IsCoassociative",
         IsAlgebroid );
-DeclareProperty( "IsCoassociative",
-        IsCategoryOfAlgebroidsObject );
 
 ####################################
 #
@@ -239,61 +209,6 @@ DeclareAttribute( "Parity",
 DeclareOperation( "POW",
         [ IsAlgebroid, IsInt ] );
 
-DeclareOperation( "\*",
-        [ IsAlgebroid, IsAlgebroid ] );
-
-DeclareOperation( "TrivialAlgebroid",
-        [ IsHomalgRing, IsString ] );
-
-DeclareOperation( "TensorProductOnObjects",
-        [ IsAlgebroid, IsAlgebroid ] );
-
-DeclareOperation( "LeftUnitorInverseAsFunctor",
-        [ IsAlgebroid ] );
-
-DeclareOperation( "LeftUnitorAsFunctor",
-        [ IsAlgebroid ] );
-
-DeclareOperation( "RightUnitorInverseAsFunctor",
-        [ IsAlgebroid ] );
-
-DeclareOperation( "RightUnitorAsFunctor",
-        [ IsAlgebroid ] );
-
-DeclareOperation( "AssociatorLeftToRightWithGivenTensorProductsAsFunctor",
-        [ IsAlgebroid, IsAlgebroid, IsAlgebroid, IsAlgebroid, IsAlgebroid ] );
-
-DeclareOperation( "AssociatorRightToLeftWithGivenTensorProductsAsFunctor",
-        [ IsAlgebroid, IsAlgebroid, IsAlgebroid, IsAlgebroid, IsAlgebroid ] );
-
-#! @Description
-#!  Construct the canonical twist from <A>A</A> $\otimes$ <A>B</A> to <A>B</A> $\otimes$ <A>A</A>
-#! @Arguments A, B
-#! @Returns a &CAP; functor
-DeclareOperation( "Twist",
-        [ IsAlgebroid, IsAlgebroid ] );
-
-#! @Description
-#!  Given an object <A>a</A> in an algebroid A and an object <A>b</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of a and b in T.
-#! @Arguments a, b, T
-#! @Returns a morphism in a &CAP; category
-DeclareOperation( "ElementaryTensor",
-        [ IsCapCategoryObjectInAlgebroid, IsCapCategoryObjectInAlgebroid, IsAlgebroid ] );
-
-#! @Description
-#!  Given an object <A>a</A> in an algebroid A and a morphism <A>g</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of a and g in T.
-#! @Arguments a, g, T
-#! @Returns a morphism in a &CAP; category
-DeclareOperation( "ElementaryTensor",
-        [ IsCapCategoryObjectInAlgebroid, IsCapCategoryMorphismInAlgebroid, IsAlgebroid ] );
-
-#! @Description
-#!  Given a morphism <A>f</A> in an algebroid A and an object <A>b</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of f and b in T.
-#! @Arguments f, b, T
-#! @Returns a morphism in a &CAP; category
-DeclareOperation( "ElementaryTensor",
-        [ IsCapCategoryMorphismInAlgebroid, IsCapCategoryObjectInAlgebroid, IsAlgebroid ] );
-
 DeclareAttribute( "BijectionBetweenPairsAndElementaryTensors",
         IsQuiverAlgebra );
 
@@ -309,6 +224,7 @@ DeclareAttribute( "DecompositionOfMorphismInSquareOfAlgebroid",
 #
 ####################################
 
+#! @Arguments e
 DeclareOperation( "DecomposeQuiverAlgebraElement",
         [ IsQuiverAlgebraElement ] );
 
@@ -326,6 +242,35 @@ DeclareOperation( "ApplyToQuiverAlgebraElement",
 DeclareOperation( "ApplyToQuiverAlgebraElement",
         [ IsCapFunctor, IsQuiverAlgebraElement ] );
 
+#! @Arguments k, str
+DeclareOperation( "TrivialAlgebroid",
+        [ IsHomalgRing, IsString ] );
+
+#! @Arguments A, B
+DeclareOperation( "\*",
+        [ IsAlgebroid, IsAlgebroid ] );
+
+#! @Description
+#!  Given an object <A>a</A> in an algebroid A and an object <A>b</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of a and b in T.
+#! @Arguments a, b, T
+#! @Returns a morphism in a &CAP; category
+DeclareOperation( "ElementaryTensor",
+        [ IsCapCategoryObjectInAlgebroid, IsCapCategoryObjectInAlgebroid, IsAlgebroid ] );
+
+#! @Description
+#!  Given an object <A>a</A> in an algebroid A and a morphism <A>g</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of a and g in T.
+#! @Arguments a, g, T
+#! @Returns a morphism in a &CAP; category
+DeclareOperation( "ElementaryTensor",
+        [ IsCapCategoryObjectInAlgebroid, IsCapCategoryMorphismInAlgebroid, IsAlgebroid ] );
+
+#! @Description
+#!  Given a morphism <A>f</A> in an algebroid A and an object <A>b</A> in an algebroid B and the tensor product <A>T</A> of A and B, return the tensor product of f and b in T.
+#! @Arguments f, b, T
+#! @Returns a morphism in a &CAP; category
+DeclareOperation( "ElementaryTensor",
+        [ IsCapCategoryMorphismInAlgebroid, IsCapCategoryObjectInAlgebroid, IsAlgebroid ] );
+
 #! @Description
 #! The ouput is the LaTeX string of the object <A>o</A>.
 #! @Arguments o
@@ -350,18 +295,6 @@ DeclareGlobalFunction( "ADD_FUNCTIONS_FOR_HOM_STRUCTURE_OF_ALGEBROID" );
 
 DeclareGlobalFunction( "ADD_FUNCTIONS_FOR_RANDOM_METHODS_OF_ALGEBROID" );
 
-DeclareOperation( "CategoryOfAlgebroids",
-                  [ IsHomalgRing, IsString ] );
-
-DeclareAttribute( "CategoryOfAlgebroidsObject",
-                  IsAlgebroid );
-
-DeclareOperation( "CategoryOfAlgebroidsMorphism",
-                  [ IsCategoryOfAlgebroidsObject, IsAlgebroidMorphism, IsCategoryOfAlgebroidsObject ] );
-
-DeclareOperation( "CategoryOfAlgebroidsMorphism",
-                  [ IsAlgebroidMorphism ] );
-
 #! @Description
 #!  Construct the algebroid associated to the path $R$-algebra <A>Rq</A>
 #!  of the quiver $q$ modulo the relations <A>L</A> as an $R$-linear category.
@@ -477,9 +410,3 @@ DeclareOperation( "MorphismInAlgebroid",
 #! @Arguments path, A
 #! @Returns a morphism in a &CAP; category
 DeclareOperation( "\/", [ IsQuiverAlgebraElement, IsAlgebroid ] );
-
-DeclareAttribute( "AsCapCategory",
-        IsCategoryOfAlgebroidsObject );
-
-DeclareAttribute( "AsCapFunctor",
-        IsCategoryOfAlgebroidsMorphism );