Bruno said
> Johnson ? Do you mean Johnstone?
Yes
> .......
> is almost impossible (even if only a familiarity with only the most
> basic introduction is enough). Adding "category theory" to that
> panel makes things worst as you can imagine.
>
I can certainly see that.
> Actually I have a much more rare and implausible book: an
> introductory course in category theory from Kinshasa
> University Press (Congo), quite
> nice but no more on the market
Sounds of value in many ways, especially if in say Wolof or Yoruba I
imagine, but I expect it is in French. Most books from the area must
carry a "Thus spake Ozymandias" feeling with them, I imagine. I
used to like Krio, which is a language which could roughly be
described as an English/Yoruba creole. I only speak English.
> A good book on Category Theory is the book by Robert Goldblatt
> "Topoi".
I still have Chu spaces rather than toposes in mind but Gouts used
toposes for his MWI, as I mentioned in a FOR post. My
understanding is that the two are a bit different. There are a
number of posts on the internet about it all, for
example
http://north.ecc.edu/alsani/ct01(5-8)/msg00051.html
and also
http://north.ecc.edu/alsani/ct01(5-8)/msg00053.html
I am so far puzzled rather than intrigued by any topos/Chu space
correspondences as I want to keep it all as simple yet as usable
as I can. People who like to delve in quantum theory often seem to go
to toposes but I want to avoid QT although of course
possibly can't.
> The *must* remains the MacLane's book "categories for the working
> mathematician" (takes me year to grasp just the preface, though!,
> but then I learn a lot).
Well I want to only use category theory if I can, so I tried to keep
it simple by sticking to Lawvere and Schanuel which apparently
experts find a few hours light entertainment but I find
thoughtprovoking.
.
I hope I don't need MacLane but may have to. (Barr & Wells online is
what I have and try to avoid, plus a lot of other online stuff, all I
can find).
> In relation with my work, and oversimplifying a little bit,
> categories
> appears mainly as generalisation of the modal S4, or S4Grz logics,
> and as such correspond to "first person notion"(*) and their
> intuitionistic logic.
> Contrariwise, the 3-person notions, which with comp are based on
> recursion theory, are the notion which fits the less with the
category
> approach (but with the Combinators some light appears in the dark
> ...).
>
> (*) Kripke models of S4 are multiverse with a reflexive and
> transitive relation of accessibility (between
> universes/states/observer-moments).
> A category is just the same except that more than one arrows are
> allowed among the "points/states...", and arrows must be composed.
>
Sounds as if it could be interesting but I have only a couple of books
by Boolos (and perhaps irrelevantly "Forever Undecided" though years
ago I did a bit of logic from Smullyan's "Theory of Formal systems"
monograph which unfortunately now seems to have gone the way of
all good books).
----- Original Message -----
From: "Bruno Marchal" <marchal.domain.name.hidden>
To: "uv" <uv.domain.name.hidden>
Cc: <everything-list.domain.name.hidden>
Sent: Wednesday, November 09, 2005 3:11 PM
Subject: Re: Question for Bruno
>
> Le 08-nov.-05, à 18:48, uv a écrit :
>
> > Bruno wrote
> >
> >> I don't know about the work of Heather and Rossiter, except some
> >> thought on quantum computation I just found by Googling. Perhaps
you
> >> could elaborate a little bit.
> >
> > I can answer you briefly on that one immediately by giving URL
> > http://computing.unn.ac.uk/staff/CGNR1/advstudiesmathsmonism.pdf
> > Please let me know if it disappears before you get there, nowadays
> > they sometimes do unfortunately.
>
>
> I got it and have printed it. Interesting (especially for the
Category
> Theory minded people, which I am a little bit) but I do think it is
a
> little bit out of topic, at least for the moment. In my "Brussels'
> thesis" I have use a bit of category theory, but I have decided to
> suppress it when I realized that asking referees simultaneous
> knowledge in
>
> basic cognitive science/philosophy of mind,
> + mathematical logic
> + quantum theory
>
> is almost impossible (even if only a familiarity with only the most
> basic introduction is enough). Adding "category theory" to that
panel
> makes things worst as you can imagine.
>
>
>
>
>
>
> > That is very close to implying a
> > TOE. My own group is http://groups.yahoo.com/group/ttj It also
> > gives my blog and URL.
> >
> > Some work has also been done by Heather and Rossiter on quantum
> > computing, with some comments on Deutsch's work.
> >
> > By the way Johnson
>
>
> Johnson ? Do you mean Johnstone?
>
>
> > seems to be the really important man in category
> > theory, "Sketching the Elephant" being the big book but afraid I
am
> > still reading Lawvere and Schanuel
>
>
>
> That is a good one. A very rare elementary introduction to category
> theory.
> Actually I have a much more rare and implausible book: an
introductory
> course in category theory from Kinshasa University Press (Congo),
quite
> nice but no more on the market. I have also the notes by Lawvere
before
> Shanuel makes the book.
> I really love category theory (especially for logic and computer
> science), and eventually, when I will come back to the combinators
(if
> I do) category will appears naturally by themselves, but I do think
it
> could be premature now.
> A good book on Category Theory is the book by Robert Goldblatt
"Topoi".
> Some categorist (like Johnstone) criticize it, because it does not
> stick on pure diagrammatic chasing, but then Goldblatt is a (modal)
> logician, and actually it is that which makes the book
understandable
> (at least for logician).
> The *must* remains the MacLane's book "categories for the working
> mathematician" (takes me year to grasp just the preface, though!,
but
> then I learn a lot).
>
> In relation with my work, and oversimplifying a little bit,
categories
> appears mainly as generalisation of the modal S4, or S4Grz logics,
and
> as such correspond to "first person notion"(*) and their
intuitionistic
> logic.
> Contrariwise, the 3-person notions, which with comp are based on
> recursion theory, are the notion which fits the less with the
category
> approach (but with the Combinators some light appears in the dark
...).
>
> (*) Kripke models of S4 are multiverse with a reflexive and
transitive
> relation of accessibility (between
universes/states/observer-moments).
> A category is just the same except that more than one arrows are
> allowed among the "points/states...", and arrows must be composed.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
Received on Thu Nov 10 2005 - 01:31:30 PST