From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4664 Path: news.gmane.org!not-for-mail From: vs27@mcs.le.ac.uk Newsgroups: gmane.science.mathematics.categories Subject: Re: Matrices Category Date: 16 Oct 2008 15:12:21 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 X-Trace: ger.gmane.org 1241020089 14283 80.91.229.2 (29 Apr 2009 15:48:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:48:09 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Oct 17 11:41:23 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 17 Oct 2008 11:41:23 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KqqNr-0006FC-Qw for categories-list@mta.ca; Fri, 17 Oct 2008 11:32:55 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 21 Original-Lines: 66 Xref: news.gmane.org gmane.science.mathematics.categories:4664 Archived-At: 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" >To: >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 >> >> > > > > -------------------------------------------------------------------------------- > > > >No virus found in this incoming message. >Checked by AVG - http://www.avg.com >Version: 8.0.173 / Virus Database: 270.8.0/1724 - Release Date: 14/10/2008 >02:02 > > > >