Re: Some books on category and topos theory

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Tue, 9 Jul 2002 20:08:31 +0200

At 9:24 -0700 9/07/2002, Tim May wrote:
>Reading styles differ, but I have come to favor the "hawk spiral." I
>see hawks spiralling in the thermals near my house, and this is how
>I like to learn. I read something from one book, think, read from
>another, think, try to compare what the authors are saying, read
>from another, go back to the earlier book and read more, and so on.
>A helix, covering the same material many times.


I have always read books in this way (except courses and novels).
In each field I'm interested in I have master books I read and reread
and satellites I consult and reconsult.
Sometimes I am not sure if I exist only but as a slave of dormant ideas
in books manipulating me for spreading in some ways ...
My books are like butterflies jumping from tables to sofas, following
me everywhere trying to exchange ideas, linking notions, etc. I am
only an humble servitor ... :)



>And much of what Tegmark outlines in his large chart can be
>dramatically simplified and abstracted.


And we need to do that! because we are distributed in the tegmark
big structure in such a way that from our local views, the global
accessible view is mathematically more rich than the big structure!
(well more on that later).


>(Aside: I believe this is a big part of what thinking is about:
>applying thoughts/concepts/morphisms/etc. from one area to another.
>Perhaps category theory will push AI in new ways.


Part of it, sure. Most "explanations" are morphism in known structures.


>Everything seemed directly related to problems which had fascinated
>me for decades. Some of these issues I hope I have hinted at here.
>
>It was almost as if category and topos theory had been invented just
>for me....an exaggeration, but it captures my sense of wonder. I
>haven't been this excited about a new area in more than a decade. I
>expect I'll be doing something in this area for at least the _next_
>decade.
>
>My apologies if this explanation of enthusiasm is too personal for
>you the reader, but I think enthusiasm is a good thing.


Me too. Now, I feel almost like you about ... knot theory.
And this fit well with your cat-enthusiasm, for knot theory is
a reservoir of beautiful and TOE-relevant categories
(the monoidal one). I've just
ordered Yetter's book: functorial(*) knot theory. It is the number 24
of Kauffman series on Knots and Everything (sic) at World
Scient. Publ Co. A series which could be a royal series for this list ...
May I recommand the n° 1, by Louis Kauffman himself: knots and physics?
A must for the (quantum) toes, and (I speculate now) the comp toe too!

I knew Yetter's work a long time ago when I read his paper on
the semantics on non commutative girard linear logic.
Unfortunately, later, the Z logics gave me a (weakening) of
quantum logic (the von neumann one), which
Yetter dismisses in that paper, so I did dismiss Yetter ...
Now I know the z logics really should have "tensorial semantics",
sort of many related (glued) von neumann type of logics (which are
themselves atlases of boolean logics).
But where (in Zs logic) those damned tensorial categories come from???
Knots gives hints!!! This would explain the geometrical appearance
of realities.

Bruno

(*) For the other: "functorial" really means categorial. Functors are
the morphisms between categories. The first chapter of Yetter's book
is an intro to category theory, the second one, on Knot theory, ...
Received on Tue Jul 09 2002 - 11:05:31 PDT