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