RE : categories: additions

["Joyal, André" <joyal.andre@uqam.ca>]

Michael Barr wrote:

>I would add something between 2 and 3 about Triples (allright, 
>monads) and Equational theories.

I agree. Let me expand the list further:

1) Algebraic topology and homological algebra
2) Abelian categories
3) Adjoint functors and monads
4) Algebraic geometry and topos theory
5) General universal algebra
6) Limit sketches and locally presentable categories
7) Categorical logic
8) Categorical model theory
9) Homotopical algebra
10) Elementary toposes theory and set theory
11) Monoidal categories and enriched category theory
12) General tensor algebras and coalgebras
13) Category theory and computer science
14) Quantum field theory
15) Higher categories and homotopy theory


Best,
André



-------- Message d'origine--------
De: Michael Barr [mailto:barr@math.mcgill.ca]
Date: lun. 21/12/2009 14:20
À: Joyal, André
Cc: categories@mta.ca
Objet : Re: categories: additions
 
I would add something between 2 and 3 about Triples (allright, 
monads) and Equational theories.

Here is an example of the sort of thing we are up against.  A colleague 
called me this morning because a student had taken a set of notes (in 
French) on his course and was interested in publishing it.  My colleague 
had an objection because in describing conformal isomorphism from the 
complex plane (or maybe sphere) to itself, the student had used the word 
"towards" (vers) instead of "on".  His objection was that a conformal 
isomorphism was something between two spaces, not from one to the other. 
My answer was a specific such map was a map from one to the other.  His 
reply essentially was, "Oh, it's category theory language.  Well, I won't 
allow any of that in MY notes. No analyst would use that language."

Michael


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