"' Mat " "'F " is a concrete skeleton category for the choosing a basis in ever finite-dimensional vector space " V " over " F "; matrices'elements represent these mappings with respect to the chosen bases; and likewise the kronecker product is the representation of the tensor product in the chosen bases.
22.
In the language of Category theory, the mixed-product property of the Kronecker product ( and more general tensor product ) shows that the category "'Mat " "'F " of matrices over a field " F ", is in fact a bicategory, with objects natural numbers " n ", morphisms are " n "-by-" m " matrices with entries in " F ", composition is given by matrix multiplication, identity arrows are simply identity matrices " I n ", and the tensor product is given by the Kronecker product.
23.
In the language of Category theory, the mixed-product property of the Kronecker product ( and more general tensor product ) shows that the category "'Mat " "'F " of matrices over a field " F ", is in fact a bicategory, with objects natural numbers " n ", morphisms are " n "-by-" m " matrices with entries in " F ", composition is given by matrix multiplication, identity arrows are simply identity matrices " I n ", and the tensor product is given by the Kronecker product.
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