From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3263 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: [Fwd: du Sautoy] Date: Thu, 20 Apr 2006 02:51:12 +0200 (CEST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019191 7964 80.91.229.2 (29 Apr 2009 15:33:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:33:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Apr 20 10:23:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Apr 2006 10:23:23 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWZ1l-0002QZ-4v for categories-list@mta.ca; Thu, 20 Apr 2006 10:16:57 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 61 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:3263 Archived-At: Dear Steve, > One of the basic expositional problems for teaching CT in computer > science is that our students do not have the body of mathematical > experience that Mac Lane presumed. I don't think that this is the problem. There are quite a few areas in CS (mainly semantics) where it is even impossible to formulate the problem when not having the language of CT available. Paradigmatic example being solution of recursive domain equations. In my regular course on semantics I introduce category theory by need and some of those people then attend my course on category theory and categorical logic (all available on my home page if you want to look). One certainly need not know a lot about algebra of geometry for these purposes. The problem rather is that most students of CS are not open to any theory whatsoever be it categorical or not. BTW another example are socalled "effects" (i.e. something fairly applied and "impure" if you want). For modelling them appropriately one needs either monads or cpo-enriched Lawvere theories. Maybe what you deplore is the absence of SIMPLE examples from CS. Well, I think one can use posets, graphs, monoids, abelian groups, fields etc. What's more problematic is the usual ignorance of simple topological examples. Maybe a bit of analysis (done properly) would do them good? Thomas