‣ ZGradedClosureCategoryWithBounds( C, str ) | ( operation ) |
Returns: a CAP category
Construct the \(\mathbb{Z}\)-graded closure of the category C with bounds. The string str can be either "lower", "upper", or "both", implementing the three constructors:
PositivelyZGradedClosureCategory,
NegativelyZGradedClosureCategory,
FinitelyZGradedClosureCategory,
respectively.
‣ ObjectInZGradedClosureCategoryWithBounds( ZC, L ) | ( operation ) |
‣ ObjectInZGradedClosureCategoryWithBounds( ZC, f, lower_bound, upper_bound ) | ( operation ) |
‣ ObjectInZGradedClosureCategoryWithBounds( ZC, M, degree ) | ( operation ) |
‣ ObjectInZGradedClosureCategoryWithBounds( ZC, M ) | ( operation ) |
‣ ObjectInZGradedClosureCategoryWithBounds( L ) | ( operation ) |
Returns: a CAP object
Construct an object in the bounded \(\mathbb{Z}\)-graded category ZC using the Z-function L.
‣ MorphismInZGradedClosureCategoryWithBounds( S, L, T ) | ( operation ) |
‣ MorphismInZGradedClosureCategoryWithBounds( S, f, T ) | ( operation ) |
‣ MorphismInZGradedClosureCategoryWithBounds( S, phi, degree, T ) | ( operation ) |
Returns: a CAP morphism
Construct a morphism in a bounded \(\mathbb{Z}\)-graded category.
‣ ComponentInclusionMorphism( M, chi, degree, i ) | ( operation ) |
‣ ComponentInclusionMorphism( M, chi, i ) | ( operation ) |
‣ ComponentInclusionMorphism( M, degree ) | ( operation ) |
Returns: a CAP morphism
‣ DiagonalEmbeddingWithGivenDegrees( M, degrees ) | ( operation ) |
‣ DiagonalEmbedding( M ) | ( operation ) |
‣ DiagonalEmbedding( S, M ) | ( operation ) |
‣ ActiveLowerBound( c ) | ( operation ) |
Returns: an integer or infinity
The active lower bound of the cell (=object or morphism) c.
‣ SetActiveLowerBound( c, lower_bound ) | ( operation ) |
Returns: an integer or infinity
Set the active lower bound of the cell (=object or morphism) c to lower_bound if it is greater than the active lower bound, and return it.
‣ ActiveUpperBound( c ) | ( operation ) |
Returns: an integer or infinity
The active upper bound of the cell (=object or morphism) c.
‣ SetActiveUpperBound( c, upper_bound ) | ( operation ) |
Returns: an integer or infinity
Set the active upper bound of the cell (=object or morphism) c to upper_bound if it is less than the active upper bound, and return it.
‣ TensorProductIndices( A, B ) | ( operation ) |
Returns: a function
Returns the function f: n |-> [ ActiveLowerBound( A ) .. n - ActiveLowerBound( B ) ] over which to run the tensor product summation A[i] \(\otimes\) B[n - i] (\(i \in f(n)\)) for (A \(\otimes\) B)[n].
‣ TensorProductIndices( A, B ) | ( operation ) |
Returns: a pair of functions
Returns two functions over which to run the tensor product summation for (A \(\otimes\) (B \(\otimes\) C))[n] resp. for ((A \(\otimes\) B) \(\otimes\) C)[n].
‣ []( c, n ) | ( operation ) |
Returns: a CAP category
The i-th object of the infinite list underlying the cell (=object or morphism) c.
‣ CertainDegreePart( c, n ) | ( operation ) |
Returns: a CAP category
The i-th object of the infinite list(s) underlying the cell resp. list c.
‣ Sublist( c, L ) | ( operation ) |
Returns: a CAP category
The L-th sublist of the infinite list underlying the cell (=object or morphism) c.
‣ IsZGradedClosureCategoryWithBounds( object ) | ( filter ) |
Returns: true or false
The GAP category of Z-graded categories with bounds.
‣ IsCellInZGradedClosureCategoryWithBounds( object ) | ( filter ) |
Returns: true or false
The GAP category of cells in a Z-graded category with bounds.
‣ IsObjectInZGradedClosureCategoryWithBounds( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a Z-graded category with bounds.
‣ IsMorphismInZGradedClosureCategoryWithBounds( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a Z-graded category with bounds.
‣ UnderlyingCategory( UC ) | ( attribute ) |
Return the category \(C\) underlying the Z-graded category with bounds category ZC := BoundedZGradedCategory( \(C\) )).
‣ UnderlyingZFunctionAndBounds( obj ) | ( attribute ) |
Returns: a pair including a Z-function and a pair of integers
The \(\mathbb{Z}\)-function underlying the object obj.
‣ UnderlyingZFunction( mor ) | ( attribute ) |
Returns: a Z-function
The \(\mathbb{Z}\)-function underlying the morphism mor.
‣ NonZeroParts( object ) | ( attribute ) |
Returns: a list
The support of the object c.
‣ NonZeroDegrees( object ) | ( attribute ) |
Returns: a list
The list of degrees of the support of the object c.
‣ NonZeroDegreesHull( object ) | ( attribute ) |
Returns: a list
A list of integers containing the list of degrees of the support of the object c.
‣ NonZeroPartsWithDegrees( object ) | ( attribute ) |
Returns: a list
‣ SupportWithDegrees( object ) | ( attribute ) |
Returns: a list
‣ SupportWithDegreesWithGivenDegrees( object, L ) | ( operation ) |
Like SupportWithDegrees but only considers the degrees in the given list L.
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