Re: Matrices Category

["R Brown" <ronnie.profbrown@btinternet.com>]

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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