‣ IsIntrinsicCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of an intrinsic CAP category.
‣ IsCapCategoryIntrinsicCell( arg ) | ( filter ) |
Returns: true or false
The GAP category of intrinsic cells in an intrinsic CAP category.
‣ IsCapCategoryIntrinsicObject( arg ) | ( filter ) |
Returns: true or false
The GAP category of intrinsic objects in an intrinsic CAP category.
‣ IsCapCategoryIntrinsicMorphism( arg ) | ( filter ) |
Returns: true or false
The GAP category of intrinsic morphisms in an intrinsic CAP category.
‣ CanonicalizeIfZero | ( filter ) |
‣ IsSafeForSideEffects( arg ) | ( property ) |
Returns: true or false
‣ CanonicalizedToZero( arg ) | ( property ) |
Returns: true or false
‣ IntrinsifyObject( C, o ) | ( operation ) |
Returns: an object in a CAP-category
Create an intrinsic object out of the object o.
‣ Intrinsify( C, o ) | ( operation ) |
Returns: an object in a CAP-category
The default method is IntrinsifyObject. This is the method to overload depending on the context.
‣ IntrinsifyMorphism( m, s, i, t, j ) | ( operation ) |
‣ Intrinsify( m, s, i, t, j ) | ( operation ) |
‣ Intrinsify( C, m ) | ( operation ) |
Returns: a morphism in a CAP-category
Create out of the morphism m an intrinsic morphism with source CertainCell(s,i) and target CertainCell(t,j). Create out of the morphism m an intrinsic morphism with source CertainCell(s,i) and target CertainCell(t,j). In the two argument version create an intrinsic morphism out of the morphism m after intrinsifying its source and target.
‣ Intrinsify( F, name, A, B ) | ( operation ) |
‣ Intrinsify( F, A, B ) | ( operation ) |
‣ Intrinsify( F, name, A ) | ( operation ) |
‣ Intrinsify( F, A ) | ( operation ) |
Intrinsify a functor ... Intrinsify a functor ... Intrinsify an endofunctor ... Intrinsify an endofunctor ...
‣ Intrinsify( eta, name, A, B ) | ( operation ) |
‣ Intrinsify( eta, A, B ) | ( operation ) |
Intrinsify a natural transformation Intrinsify a natural transformation
‣ TurnAutoequivalenceIntoIdentityFunctor( eta ) | ( operation ) |
Returns: a functor
Turn the range of the natural isomorphism eta into the identity functor and turn eta into the identity natural transformation.
‣ CanonicalizeZeroObjectsAsIdentityFunctor( category ) | ( attribute ) |
Returns: a functor
Turn FunctorCanonicalizeZeroObjects(category) into the identity functor.
‣ CanonicalizeZeroMorphismsAsIdentityFunctor( category ) | ( attribute ) |
Returns: a CAP functor
Turn FunctorCanonicalizeZeroMorphisms(category) into the identity functor.
‣ IntrinsicCategory( C ) | ( operation ) |
Returns: a CAP category
Create in the sense explained below an "intrinsic" category out of the category C. The procedure understands five options:
strict (true or false);
filter_obj (a filter used to define the type of intrinsified objects);
filter_mor (a filter used to define the type of intrinsified morphisms);
filter_end (a filter used to define the type of intrinsified endomorphisms);
todo_func (a function which does not need to return anything).
If strict=true then the CAP's congruence relation on the \(Hom\)-setoids is divided out. The argument todo_func is a function which will be applied in all CAP constructions CAP_oper producing a morphism to the argument list of CAP_oper (as first argument) and the output of CAP_oper (as second argument). If the option strict is not specified it defaults to true. If filter_obj is not specified it defaults to IsCapCategoryIntrinsicObject. If filter_mor is not specified it defaults to IsCapCategoryIntrinsicMorphism. If filter_end is not specified it defaults to IsCapCategoryIntrinsicMorphism. If todo is not specified it defaults to ReturnNothing.
‣ UnderlyingCategory( C ) | ( attribute ) |
The category underlying the intrinsic category C.
‣ IsLockedObject( c ) | ( operation ) |
Check whether the intrinsic object c is locked or not.
‣ PositionOfLastStoredCell( c ) | ( operation ) |
Return the position of the last stored cell underlying the intrinsic cell c.
‣ CertainCell( o, i ) | ( operation ) |
Return the i-th object underlying the intrinsic object o.
‣ CertainCell( m, i, j, k ) | ( operation ) |
Return the (i,j,k)-th morphism underlying the intrinsic cell m.
‣ CertainCell( m, i, j ) | ( operation ) |
Return the (i,j)-th morphism underlying the intrinsic cell m.
‣ PositionOfActiveCell( c ) | ( operation ) |
Return the position of the active cell underlying the intrinsic cell c.
‣ SetPositionOfActiveCell( c, p ) | ( operation ) |
Set the position of the active cell underlying the intrinsic cell c using p.
‣ ActiveCell( c ) | ( operation ) |
Return the active cell underlying the intrinsic cell c.
‣ AddTransitionIsomorphism( o, s, eta ) | ( operation ) |
Add the isomorphism eta to the record of transition isomorphisms. Source( eta ) must be equal to CertainCell( o, s ).
‣ AddTransitionIsomorphism( o, eta, t ) | ( operation ) |
‣ AddTransitionIsomorphism( o, s, eta, t ) | ( operation ) |
In the second version the Range( eta ) must be equal to CertainCell( o, t ). In the third version the Range( eta ) must be equal to CertainCell( o, t ) and the Source( eta ) must be equal to CertainCell( o, s ).
‣ TransitionIsomorphism( o, s, t ) | ( operation ) |
Return the transition isomorphism of the intrinsic object o at position (s,t).
‣ AddToIntrinsicMorphism( mor, m, s, t ) | ( operation ) |
Add the morphism m to the intrinsic morphism mor at position [ s, t, ? ].
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