@@ -28,21 +28,84 @@ end );
2828# #
2929InstallMethod( FreydCategory,
3030 [ IsCategoryOfGradedRows ] ,
31- function ( underlying_category )
32- local category, graded_ring;
33-
34- graded_ring := UnderlyingGradedRing( underlying_category );
35-
36- category := FREYD_CATEGORY( underlying_category, Concatenation( " Category of f.p. graded left modules over "
37-
38- SetFilterObj( category, IsFpGradedLeftModules );
39-
40- AddObjectRepresentation( category, IsFreydCategoryObject and HasRelationMorphism and IsFpGradedLeftModulesObject );
41-
42- AddMorphismRepresentation( category, IsFreydCategoryMorphism and HasUnderlyingMorphism and IsFpGradedLeftModulesMorphism );
43-
44- return category;
45-
31+
32+ function ( underlying_category )
33+ local graded_ring, freyd, object_constructor, modeling_tower_object_constructor, object_datum, modeling_tower_object_datum, morphism_constructor, modeling_tower_morphism_constructor, morphism_datum, modeling_tower_morphism_datum, wrapper;
34+
35+ graded_ring := UnderlyingGradedRing( underlying_category );
36+
37+ freyd := FREYD_CATEGORY( underlying_category );
38+
39+ object_constructor := function ( cat, relation_morphism )
40+
41+ return CreateCapCategoryObjectWithAttributes( cat, RelationMorphism, relation_morphism );
42+
43+ end ;
44+
45+ modeling_tower_object_constructor := function ( cat, relation_morphism )
46+
47+ return CreateCapCategoryObjectWithAttributes( ModelingCategory( cat ), RelationMorphism, relation_morphism );
48+
49+ end ;
50+
51+ object_datum := function ( cat, object )
52+
53+ return RelationMorphism( object );
54+
55+ end ;
56+
57+ modeling_tower_object_datum := function ( cat, object )
58+
59+ return RelationMorphism( object );
60+
61+ end ;
62+
63+ morphism_constructor := function ( cat, source, underlying_morphism, range )
64+
65+ return CreateCapCategoryMorphismWithAttributes( cat, source, range, UnderlyingMorphism, underlying_morphism );
66+
67+ end ;
68+
69+ modeling_tower_morphism_constructor := function ( cat, source, underlying_morphism, range )
70+
71+ return CreateCapCategoryMorphismWithAttributes( ModelingCategory( cat ), source, range, UnderlyingMorphism, underlying_morphism );
72+
73+ end ;
74+
75+ morphism_datum := function ( cat, morphism )
76+
77+ return UnderlyingMorphism( morphism );
78+
79+ end ;
80+
81+ modeling_tower_morphism_datum := function ( cat, morphism )
82+
83+ return UnderlyingMorphism( morphism );
84+
85+ end ;
86+
87+ wrapper := WrapperCategory( freyd, rec (
88+ name := Concatenation( " Category of f.p. graded left modules over "
89+ category_filter := IsFreydCategory and IsFpGradedLeftModules,
90+ category_object_filter := IsFreydCategoryObject and HasRelationMorphism and IsFpGradedLeftModulesObject,
91+ category_morphism_filter := IsFreydCategoryMorphism and HasUnderlyingMorphism and IsFpGradedLeftModulesMorphism,
92+ object_constructor := object_constructor,
93+ object_datum := object_datum,
94+ morphism_constructor := morphism_constructor,
95+ morphism_datum := morphism_datum,
96+ modeling_tower_object_constructor := modeling_tower_object_constructor,
97+ modeling_tower_object_datum := modeling_tower_object_datum,
98+ modeling_tower_morphism_constructor := modeling_tower_morphism_constructor,
99+ modeling_tower_morphism_datum := modeling_tower_morphism_datum,
100+ # enforce defaults
101+ only_primitive_operations := false ,
102+ wrap_range_of_hom_structure := false ,
103+ ) );
104+
105+ SetUnderlyingCategory( wrapper, underlying_category );
106+
107+ return wrapper;
108+
46109end );
47110
48111# compute the category S-fpgrmod for a toric variety
@@ -58,19 +121,82 @@ end );
58121# #
59122InstallMethod( FreydCategory,
60123 [ IsCategoryOfGradedColumns ] ,
61- function ( underlying_category )
62- local category, graded_ring;
63-
64- graded_ring := UnderlyingGradedRing( underlying_category );
65-
66- category := FREYD_CATEGORY( underlying_category, Concatenation( " Category of f.p. graded right modules over "
67-
68- SetFilterObj( category, IsFpGradedRightModules );
69-
70- AddObjectRepresentation( category, IsFreydCategoryObject and HasRelationMorphism and IsFpGradedRightModulesObject );
71-
72- AddMorphismRepresentation( category, IsFreydCategoryMorphism and HasUnderlyingMorphism and IsFpGradedRightModulesMorphism );
73-
74- return category;
75-
124+
125+ function ( underlying_category )
126+ local graded_ring, freyd, object_constructor, modeling_tower_object_constructor, object_datum, modeling_tower_object_datum, morphism_constructor, modeling_tower_morphism_constructor, morphism_datum, modeling_tower_morphism_datum, wrapper;
127+
128+ graded_ring := UnderlyingGradedRing( underlying_category );
129+
130+ freyd := FREYD_CATEGORY( underlying_category );
131+
132+ object_constructor := function ( cat, relation_morphism )
133+
134+ return CreateCapCategoryObjectWithAttributes( cat, RelationMorphism, relation_morphism );
135+
136+ end ;
137+
138+ modeling_tower_object_constructor := function ( cat, relation_morphism )
139+
140+ return CreateCapCategoryObjectWithAttributes( ModelingCategory( cat ), RelationMorphism, relation_morphism );
141+
142+ end ;
143+
144+ object_datum := function ( cat, object )
145+
146+ return RelationMorphism( object );
147+
148+ end ;
149+
150+ modeling_tower_object_datum := function ( cat, object )
151+
152+ return RelationMorphism( object );
153+
154+ end ;
155+
156+ morphism_constructor := function ( cat, source, underlying_morphism, range )
157+
158+ return CreateCapCategoryMorphismWithAttributes( cat, source, range, UnderlyingMorphism, underlying_morphism );
159+
160+ end ;
161+
162+ modeling_tower_morphism_constructor := function ( cat, source, underlying_morphism, range )
163+
164+ return CreateCapCategoryMorphismWithAttributes( ModelingCategory( cat ), source, range, UnderlyingMorphism, underlying_morphism );
165+
166+ end ;
167+
168+ morphism_datum := function ( cat, morphism )
169+
170+ return UnderlyingMorphism( morphism );
171+
172+ end ;
173+
174+ modeling_tower_morphism_datum := function ( cat, morphism )
175+
176+ return UnderlyingMorphism( morphism );
177+
178+ end ;
179+
180+ wrapper := WrapperCategory( freyd, rec (
181+ name := Concatenation( " Category of f.p. graded right modules over "
182+ category_filter := IsFreydCategory and IsFpGradedRightModules,
183+ category_object_filter := IsFreydCategoryObject and HasRelationMorphism and IsFpGradedRightModulesObject,
184+ category_morphism_filter := IsFreydCategoryMorphism and HasUnderlyingMorphism and IsFpGradedRightModulesMorphism,
185+ object_constructor := object_constructor,
186+ object_datum := object_datum,
187+ morphism_constructor := morphism_constructor,
188+ morphism_datum := morphism_datum,
189+ modeling_tower_object_constructor := modeling_tower_object_constructor,
190+ modeling_tower_object_datum := modeling_tower_object_datum,
191+ modeling_tower_morphism_constructor := modeling_tower_morphism_constructor,
192+ modeling_tower_morphism_datum := modeling_tower_morphism_datum,
193+ # enforce defaults
194+ only_primitive_operations := false ,
195+ wrap_range_of_hom_structure := false ,
196+ ) );
197+
198+ SetUnderlyingCategory( wrapper, underlying_category );
199+
200+ return wrapper;
201+
76202end );
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