On Mon, Oct 13, 2008 at 9:34 AM, Hugo Macedo <hugodsmacedo@gmail.com> wrote:
Hello
I'm trying to study the Category of Matrices but I found almost nothing. Do you know where I can find information about them?
I think you may have more success searching for information about the category Vect_K of vector spaces and K-linear transformations between them, where K is the field of interest (usually the reals K=R or the complex numbers K=C).
More specifically can we consider the tensor product as the product bi-functor?
In Set, the cartesian product is different from the coproduct, and the product satisfies hom(A x B, C) is isomorphic to hom(A, C^B) making Set into a cartesian closed category, a special kind of symmetric monoidal closed category; but this is not true in Vect. The product and coproduct are the same in Vect, namely the "direct sum", while the tensor product is what makes Vect into a symmetric monoidal closed category: hom(A tensor B, C) = hom(A, B -o C) where -o is linear implication. Vect also happens to be a compact closed category, which means that B -o C is isomorphic to B* tensor C. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com