Category of Matrices
Constructors a category The argument is a homalg field F. The output is the matrix category over F. Objects in this category are non-negative integers. Morphisms from a non-negative integer m to a non-negative integer n are given by m \times n matrices. a category The argument is a homalg field F. The output is the matrix category over F, constructed internally as a wrapper category of the `CategoryOfRows` of F. Only available if the package `FreydCategoriesForCAP` is available. a morphism in \mathrm{Hom}(S,R) 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. an object The arguments are a non-negative integer d and a homalg field F. The output is an object in the category of matrices over F of dimension d. This function delegates to MatrixCategoryObject. an object The arguments are a matrix category cat over a field and a non-negative integer d. The output is an object in cat of dimension d.
Attributes a homalg field The argument is a morphism \alpha in the matrix category over a homalg field F. The output is the field F. a homalg matrix The argument is a morphism \alpha in a matrix category. The output is its underlying matrix M. a homalg field The argument is an object A in the matrix category over a homalg field F. The output is the field F. a non-negative integer The argument is an object A in a matrix category. The output is the dimension of A.
GAP Categories true or false The GAP category of morphisms in the category of matrices of a field F. true or false The GAP category of objects in the category of matrices of a field F.