Subject: categories: Re: [Fwd: du Sautoy]

From: Thomas Streicher <[email-masked]>
Date: Thu, 20 Apr 2006 02:51:12 +0200 (CEST)

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