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

[Ionel <***>]

Hi, Tim:

Well, I wouldn't take too literally what the amazon site says; categories
are categories-- here it comes, an 'impredicative' statement, but I
am sure you'd follow my semantics.

Actually, of all of these books the ..."Working Mathematician" is
probably the best value as it covers so well most areas. Hope this helps.

Of course, the next best is J.P. May's Concise course book since you can
download its contents  from his website; it's amazingly compact and covers
a lot of ground that's not covered by many quite expensive books.

There will also be a new book printed soon, (and I suspect from your
viewpoint maybe even harder, but I'm sure it will be very interesting)
on Nonabelian Algebraic Topology by R. Brown.  (Do you also remember the
Higher Dimensional Algebra in Neuroscience preprint by the same author?).

Regards,

Ionel


On Tue, 1 Jun 2004 22:14:37 -0400, Tim Gwinn <***> wrote:

>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