Re: additions

[Michael Barr <barr@math.mcgill.ca>]

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

On Mon, 21 Dec 2009, Joyal, André wrote:

> In my message to John Baez, I wrote:
>
>> I can distinguish approximatly 6 major currents:
>
>> 1) Algebraic topology and homological algebra
>> 2) Abelian categories
>> 3) Algebraic Geometry and topos theory
>> 4) Logic and elementary topos theory
>> 5) Category theory and computer science
>> 6) Higher categories with homotopy theory
>
> The list is too restrictive. I would like to expand it further:
>
> 1) Algebraic topology and homological algebra
> 2) Abelian categories
> 3) Algebraic geometry and topos theory
> 4) General cartesian algebra
> 5) Categorical logic
> 6) Homotopical algebra
> 7) Elementary topos theory and set theory
> 8) Monoidal categories and enriched category theory
> 9) General tensor algebra and coalgebra
> 10) Category theory and computer science
> 11) Quantum field theory
> 12) Higher categories and homotopy theory
>
> Algebraic theories and limit sketches are included in (4).
> Multicategories, operads are included in (9).
>
> I have included Quillen homotopical algebra in (6).
>
> Best,
> André
>

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