Re: Paper on variable set theory

Re: Paper on variable set theory

[Camell Kachour]

Dear categoricists,

It is well known that higher category theory has applications in homotopy
(Work of Joyal, Lurie, Grothendieck conjecture, etc.).

May someone gives me some references about probable applications of higher
category theory in other areas ? I guess in computer science and
other areas (rewriting ? etc.), they are probably some works !?

Thank you very much to give me these references and for your help !

Best regards,
Camell.


On Sat, Dec 14, 2013 at 10:59 PM, Michael Barr <barr@math.mcgill.ca> wrote:

> Around 1986, Colin McLarty, Charles Wells, and I noticed that Scientific
> American had recently published a few articles on subjects mathematical
> and decided to try to write one on variable set theory, AKA topos theory.
> Unfortunately, that particular window at Sci Am quickly closed.  Our
> article was turned down and we forgot about it.  More recently, I decided
> it might be interesting, or at least amusing to throw it open to the
> categorical community.  The result can be found at
> ftp://ftp.math.mcgill.ca/barr/pdffiles/vst.pdf
>
> Michael
>
> --
>         Every gun that is made, every warship launched, every rocket fired
> signifies, in the final sense, a theft from those who hunger and are not
> fed, those who are cold and are not clothed. -Dwight D. Eisenhower
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Paper on variable set theory

[Ronnie Brown]

A couple of general articles, somewhat speculative,  are available from
my publication list:
http://pages.bangor.ac.uk/~mas010/publicfull.htm



130.(with T. PORTER), `The intuitions of higher dimensional algebra for
the study of structured space', Revue de Synth?se, 124 (2003)  173-203.
` UWB Math. Preprint (pdf file) <pdffiles/paris-cogn9.pdf>.


136. (with T. Porter), `Category theory and higher dimensional algebra:
potential descriptive tools in neuroscience', Proceedings of the
International Conference on Theoretical Neurobiology, Delhi, February
2003, edited by Nandini Singh, National Brain Research Centre,
Conference Proceedings 1 (2003) 80-92. pdf <pdffiles/brown-porter03_05.pdf>

You should also look at the area of concurrency theory. Running many
computers is analogous to many dimensional time.

And do a web search on "higher dimensional algebra" with for example
physics, biology, ...



Ronnie




On 17/12/2013 01:24, Camell Kachour wrote:
> Dear categoricists,
>
> It is well known that higher category theory has applications in homotopy
> (Work of Joyal, Lurie, Grothendieck conjecture, etc.).
>
> May someone gives me some references about probable applications of higher
> category theory in other areas ? I guess in computer science and
> other areas (rewriting ? etc.), they are probably some works !?
>
> Thank you very much to give me these references and for your help !
>
> Best regards,
> Camell.
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Paper on variable set theory

[Michael Barr]

Around 1986, Colin McLarty, Charles Wells, and I noticed that Scientific
American had recently published a few articles on subjects mathematical
and decided to try to write one on variable set theory, AKA topos theory.
Unfortunately, that particular window at Sci Am quickly closed.  Our
article was turned down and we forgot about it.  More recently, I decided
it might be interesting, or at least amusing to throw it open to the
categorical community.  The result can be found at
ftp://ftp.math.mcgill.ca/barr/pdffiles/vst.pdf

Michael

-- 
         Every gun that is made, every warship launched, every rocket fired
signifies, in the final sense, a theft from those who hunger and are not
fed, those who are cold and are not clothed. -Dwight D. Eisenhower



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]