About categories

[John Kennison]

Hi
Off the top of my head, the basic reference to category theory is by Saunders Mac Lane and is called "Categories for the working mathematician". For a bare bones basic category theory, I would look online (I may have a recommendation later). Beyond that, it depends on what you want to do with categories. Much of what I do involves topos theory, where a topos is a category that formally looks like the category of sets and mappings. --In sets, we have the cartesian product and the sum (or disjoint union) and equalizers (or subset where two functions agree) and function sets (the set of all functions from one set to another is itself a set, hence an object of the category of sets and the power set (or the set of all subsets of a set). These constructions must obey formal rules which determine them uniquely, if they exist. A typical example of a topos is the category of sheaves over a topological space, which is, conceptually, the category of sets whose "elements" can vary continuously over a fixed topological space. Good introductions to toposes and their uses can be found in Barr and Wells, "Toposes, triples and theories" which is available online (search for "Michael Barr" and go to his home page) and in my papers on Boolean flows, in TAC --I'll write again with more information.
--John



________________________________________
From: [hidden email] [[hidden email]] On Behalf Of Tom Johnson [[hidden email]]
Sent: Monday, August 11, 2008 10:30 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Intro

Welcome, John.  I hope you can visit Santa Fe and give us a rich briefing on category theory.

All the best,
Tom Johnson

On Mon, Aug 11, 2008 at 8:11 PM, John F. Kennison <[hidden email]<mailto:[hidden email]>> wrote:
Hi,

My name is John Kennison and I am glad to be welcomed to the Friam group. I am a retired Math professor and have been a friend and colleague of Nick Thompson's for many years. My field is category theory and I am interested in all kinds of applications of categories to other areas of math, including dynamical systems. I have been reading Rosen's "Life Itself" which seems half-baked, pretentious and badly written, but which also seems to be asking some deep and important questions. So I enjoy trying to puzzle my way through it.

I like listening to discussions about the nature of math. While I have practical experience as a mathematician and am not afraid to voice my opinions, I have done almost no philosophical  reading on this subject.

---John

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--
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J. T. Johnson
Institute for Analytic Journalism -- Santa Fe, NM USA
www.analyticjournalism.com<http://www.analyticjournalism.com>
505.577.6482(c) 505.473.9646(h)
http://www.jtjohnson.com [hidden email]<mailto:[hidden email]>

"You never change things by fighting the existing reality.
To change something, build a new model that makes the
existing model obsolete."
-- Buckminster Fuller
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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org