Re: Matrices Category

[vs27@mcs.le.ac.uk]

I am surprised that nobody suggested to Hugo
to have a look at modules/profunctors.
??


On Oct 16 2008, R Brown wrote:

>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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