Re: Categorical Foundations : Special Topics in Order, Topology, Algebra, and Sheaf Theory

[Tim Gwinn <***>]

Ionel,

Thanks for the heads-up. The description on Amazon for "Categorical
Foundations : Special Topics in Order, Topology, Algebra, and
Sheaf" says:
===
Researchers, teachers and graduate students in algebra and
topology--familiar with the very basic notions of category theory--will
welcome this categorical introduction to some of the key areas of modern
mathematics, without being forced to study category theory. Rather, each of
the eight largely independent chapters analyzes a particular subject,
revealing the power and applicability of the categorical foundations in each
case.
===
"Without being forced to study category theory"!!?? That seems remarkable!
Yet it sounds like it has some pretty in-depth topics by what you describe.
Definitely going onto my wishlist.

So far, I'm not thrilled with "Elementary Categories, Elementary Toposes". I
had expected it to be more verbose and instructive. I've not had much time
to go through it, though. Topos logic does not appear like alot of fun, and
some of the differences from classical logic seem counterintuitive. Based on
the layout of what I read in "....Working Mathematician", by comparison, I
probably should have chosen Mac Lane's newer book that you previously
recommended instead of "EC,ET". Oh well.

The May book looks pretty serious for a 'concise' course. The PDF is about
250 pgs. :)
If anyone else is interested, May's homepage is at:
http://www.math.uchicago.edu/~may/

Regards,
Tim


> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Ionel
> Sent: Tuesday, June 01, 2004 9:32 PM
> To: ***
> Subject: Categorical Foundations : Special Topics in Order, Topology,
> Algebra, and Sheaf Theory
>
>
> Tim:
>
> Another good book on category theory is the brand new (2004):
>
> Categorical Foundations : Special Topics in Order, Topology, Algebra, and
> Sheaf [Hardcover]
> By: Maria Cristina Pedicchio (Editor), Walter Tholen (Editor)
>  (~$70 new).
>
> Amongst a great deal of fundamental logical stuff it has a well-developed
> section on the category of relations, including Adjoint Relations and
> Adjunctions in general; it also introduces the Topos axioms, Sheaves,
> Algebraic Categories in a large , significant section, Heyting
> and complete
> Heyting Algebras and Logics. It's an interesting combination of advanced
> category theory and clearly written introductory sections. It pays special
> attention to Topology and generalized topology. I am happy to have bought
> this book along with J.P. May's out-of-print affordable "Concise
> Topological Algebra" (one can also obtain/ download the latter for free
> from  Professor J.P. May's own site at the University of Chicago.)
>
> Regards,
> Ionel