On any additive category A you can define a category of matrices Mat(A). The objects of Mat(A) are n-tuples A_*= (A_1, ...,A_n) for all n >= 1, of objects of A. A morphism a_**: A_* \to B_* consists of arrays of morphisms a_{ij}: A_i \to B_j (or is it the other way round? I leave you to look for the conventions). If you get the conventions right, then composition in Mat(A) is just matrix composition. The nice point about this is that Mat(A) is again an additive category, so the process can be iterated. Actually only semi-additive is needed (matrix composition does not use negatives.) The above idea essentially yields partitioned matrices (see old books on matrices). This passage A \mapsto Mat(A) ought to be available on computer software! I expect the above is in a reference somewhere! Ronnie Brown www.bangor.ac.uk/r.brown ----- Original Message ----- From: "Hugo Macedo" <hugodsmacedo@gmail.com> To: <categories@mta.ca> Sent: Monday, October 13, 2008 5:34 PM Subject: categories: Matrices Category
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?
More specifically can we consider the tensor product as the product bi-functor?
-- Hugo
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