MatrixCategoryMorphism.gd

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##                                LinearAlgebraForCAP package
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##  Copyright 2015, Sebastian Gutsche, TU Kaiserslautern
##                  Sebastian Posur,   RWTH Aachen
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#! @Chapter Category of Matrices
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#! @Section GAP Categories
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#! @Description
#! The GAP category of morphisms in the category
#! of matrices of a field $F$.
#! @Arguments object
DeclareCategory( "IsVectorSpaceMorphism",
                 IsCapCategoryMorphism and IsCellOfSkeletalCategory );

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#! @Section Constructors
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#! @Description
#! The arguments are an object $S$ in the category of matrices over a
#! homalg field $F$, a homalg matrix $M$ over $F$, and another object $R$
#! in the category of matrices over $F$.
#! The output is the morphism $S \rightarrow R$ in the category
#! of matrices over $F$ whose underlying matrix is given by $M$.
#! @Returns a morphism in $\mathrm{Hom}(S,R)$
#! @Arguments S, M, R
DeclareOperation( "VectorSpaceMorphism",
                  [ IsVectorSpaceObject, IsHomalgMatrix, IsVectorSpaceObject ] );

DeclareOperationWithCache( "VectorSpaceMorphism",
                           [ IsVectorSpaceObject, IsList, IsVectorSpaceObject ] );

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#! @Section Attributes
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#! @Description
#! The argument is a morphism $\alpha$ in the matrix category over a
#! homalg field $F$.
#! The output is the field $F$.
#! @Returns a homalg field
#! @Arguments alpha
DeclareAttribute( "UnderlyingFieldForHomalg",
                  IsVectorSpaceMorphism );

#! @Description
#! The argument is a morphism $\alpha$ in a matrix category.
#! The output is its underlying matrix $M$.
#! @Returns a homalg matrix
#! @Arguments alpha
DeclareAttribute( "UnderlyingMatrix",
                  IsVectorSpaceMorphism );

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#! @Section Arithmetics
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DeclareOperation( "\*",
                  [ IsRingElement, IsVectorSpaceMorphism ] );

DeclareOperation( "\*",
                  [ IsVectorSpaceMorphism, IsRingElement ] );