Merge pull request #1425 from TKuh/cat_first_integers

Category as first argument for `IntegerCategory`
homalg-project · Aug 16, 2023 · 6795a14 · 6795a14
2 parents f369742 + 0da18c8
commit 6795a14
Showing 1 changed file with 50 additions and 64 deletions.
diff --git a/CAP/examples/IntegerCategory.g b/CAP/examples/IntegerCategory.g
@@ -1,40 +1,37 @@
 
 LoadPackage( "CAP" );
 
-DeclareRepresentation( "IsHomalgIntegerRep",
-                       IsCapCategoryObjectRep,
-                       [ ] );
+DeclareCategory( "IsCategoryOfHomalgIntegers",
+                 IsCapCategory );
 
-BindGlobal( "TheTypeOfHomalgIntegers",
-        NewType( TheFamilyOfCapCategoryObjects,
-                IsHomalgIntegerRep ) );
+DeclareCategory( "IsObjectInCategoryOfHomalgIntegers",
+                 IsCapCategoryObject );
 
-DeclareRepresentation( "IsHomalgIntegerMorphismRep",
-                       IsCapCategoryMorphismRep,
-                       [ ] );
-
-BindGlobal( "TheTypeOfHomalgIntegerMorphism",
-        NewType( TheFamilyOfCapCategoryMorphisms,
-                IsHomalgIntegerMorphismRep ) );
+DeclareCategory( "IsMorphismInCategoryOfHomalgIntegers",
+                 IsCapCategoryMorphism );
 
 ############################
 ##
 ## Attributes
 ##
 ############################
 
-DeclareAttribute( "AsInteger",
-                  IsHomalgIntegerRep );
+DeclareAttribute( "UnderlyingInteger",
+                  IsObjectInCategoryOfHomalgIntegers );
 
 ############################
 ##
 ## Category
 ##
 ############################
 
-integer_category := CreateCapCategory( "Integers" );
+integer_category := CreateCapCategory( "HomalgIntegers",
+                                       IsCategoryOfHomalgIntegers,
+                                       IsObjectInCategoryOfHomalgIntegers,
+                                       IsMorphismInCategoryOfHomalgIntegers,
+                                       IsCapCategoryTwoCell );
 
-integer_category!.category_as_first_argument := false;
+integer_category!.category_as_first_argument := true;
 
 #############################
 ##
@@ -50,14 +47,9 @@ InstallMethodWithCache( HomalgInteger,
                         [ IsInt ],
 
   function( integer )
-    local homalg_integer;
-
-    homalg_integer := ObjectifyWithAttributes( rec( ), TheTypeOfHomalgIntegers,
-                                               AsInteger, integer );
-
-    Add( integer_category, homalg_integer );
 
-    return homalg_integer;
+    return CreateCapCategoryObjectWithAttributes( integer_category,
+                                                  UnderlyingInteger, integer );
 
 end );
 
@@ -70,51 +62,44 @@ InstallMethod( HomalgIntegerMorphism,
 
   function( source, range )
 
-    if range < source then
-
-        Error( "such a morphism does not exist" );
-
-    fi;
-
     return HomalgIntegerMorphism( HomalgInteger( source ), HomalgInteger( range ) );
 
 end );
 
 DeclareOperation( "HomalgIntegerMorphism",
-                  [ IsHomalgIntegerRep, IsHomalgIntegerRep ] );
+                  [ IsObjectInCategoryOfHomalgIntegers, IsObjectInCategoryOfHomalgIntegers ] );
 
 ##
 InstallMethodWithCache( HomalgIntegerMorphism,
-                        [ IsHomalgIntegerRep, IsHomalgIntegerRep ],
+                        [ IsObjectInCategoryOfHomalgIntegers, IsObjectInCategoryOfHomalgIntegers ],
 
   function( source, range )
-    local morphism;
 
-    if AsInteger( range ) < AsInteger( source ) then
+    if UnderlyingInteger( range ) < UnderlyingInteger( source ) then
 
         Error( "such a morphism does not exist" );
 
     fi;
 
-    morphism := ObjectifyWithAttributes( rec( ), TheTypeOfHomalgIntegerMorphism,
-                                         Source, source,
-                                         Range, range );
-
-    Add( integer_category, morphism );
-
-    return morphism;
+    return CreateCapCategoryMorphismWithAttributes( integer_category,
+                                                    source,
+                                                    range );
 
 end );
 
 ##
 AddIsCongruentForMorphisms( integer_category,
 
-  ReturnTrue );
+  function( cat, mor1, mor2 )
+
+      return true;
+
+end );
 
 ##
 AddIsZeroForMorphisms( integer_category,
 
-  function( a )
+  function( cat, a )
 
     return true;
 
@@ -123,7 +108,7 @@ end );
 ##
 AddAdditionForMorphisms( integer_category,
 
-  function( a, b )
+  function( cat, a, b )
 
     return a;
 
@@ -132,12 +117,16 @@ end );
 ##
 AddAdditiveInverseForMorphisms( integer_category,
 
-  IdFunc );
+  function( cat, mor )
+
+    return mor;
+
+end );
 
 ##
 AddZeroMorphism( integer_category,
 
-  function( a, b )
+  function( cat, a, b )
 
     return HomalgIntegerMorphism( a, b );
 
@@ -146,7 +135,7 @@ end );
 ##
 AddIdentityMorphism( integer_category,
 
-  function( obj )
+  function( cat, obj )
 
     return HomalgIntegerMorphism( obj, obj );
 
@@ -155,7 +144,7 @@ end );
 ##
 AddPreCompose( integer_category,
 
-  function( mor1, mor2 )
+  function( cat, mor1, mor2 )
 
     return HomalgIntegerMorphism( Source( mor1 ), Range( mor2 ) );
 
@@ -164,10 +153,10 @@ end );
 #
 AddFiberProduct( integer_category,
 
-  function( product_mor )
+  function( cat, product_mor )
     local pullback;
 
-    pullback := Gcd( List( product_mor, i -> AsInteger( Source( i ) ) ) );
+    pullback := Gcd( List( product_mor, i -> UnderlyingInteger( Source( i ) ) ) );
 
     return HomalgInteger( pullback );
 
@@ -176,23 +165,22 @@ end );
 ##
 AddProjectionInFactorOfFiberProductWithGivenFiberProduct( integer_category,
 
-  function( product_morx, coordinate, pullback )
+  function( cat, product_morx, coordinate, pullback )
     local range;
 
-    range := Source( product_mor[ coordinate ] );
+    range := Source( product_morx[ coordinate ] );
 
     return HomalgIntegerMorphism( pullback, range );
 
 end );
 
-
 ##
 AddPushout( integer_category,
 
-  function( product_mor )
+  function( cat, product_mor )
     local pushout;
 
-    pushout := Lcm( List( product_mor, i -> AsInteger( Range( i ) ) ) );
+    pushout := Lcm( List( product_mor, i -> UnderlyingInteger( Range( i ) ) ) );
 
     return HomalgInteger( pushout );
 
@@ -201,7 +189,7 @@ end );
 ##
 AddInjectionOfCofactorOfPushoutWithGivenPushout( integer_category,
 
-  function( product_mor, coordinate, pushout )
+  function( cat, product_mor, coordinate, pushout )
     local source;
 
     source := Range( product_mor[ coordinate ] );
@@ -213,15 +201,12 @@ end );
 ##
 AddLiftAlongMonomorphism( integer_category,
 
-  function( monomorphism, test_morphism )
+  function( cat, monomorphism, test_morphism )
 
     return HomalgIntegerMorphism( Source( test_morphism ), Source( monomorphism ) );
 
 end );
 
-##
-
-
 ###################################
 ##
 ## View
@@ -230,20 +215,21 @@ end );
 
 ##
 InstallMethod( ViewString,
-               [ IsHomalgIntegerRep ],
+               [ IsObjectInCategoryOfHomalgIntegers ],
 
   function( integer_obj )
 
-    return Concatenation( "<The integer object representing ", String( AsInteger( integer_obj ) ), ">" );
+    return Concatenation( "<The integer object representing ", String( UnderlyingInteger( integer_obj ) ), ">" );
 
 end );
 
 ##
 InstallMethod( ViewString,
-               [ IsHomalgIntegerMorphismRep ],
+               [ IsMorphismInCategoryOfHomalgIntegers ],
 
   function( integer_mor )
 
-    return Concatenation( "<", String( AsInteger( Source( integer_mor ) ) ), " -> ", String( AsInteger( Range( integer_mor ) ) ), ">" );
+    return Concatenation( "<", String( UnderlyingInteger( Source( integer_mor ) ) ), " -> ", String( UnderlyingInteger( Range( integer_mor ) ) ), ">" );
 
 end );
+