additive 2-categories and related structures?
I would be grateful for information on published or available work in this area. I am thinking of an additive category as a ring with several objects, as in Mitchell's well known paper. So in a sense am looking at 2-rings. Thanks in anticipation. Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Hi Ronnie, There is the work of Matthieu Dupont, see his page http://breckes.org/dom-en.html His PhD thesis is on abelian categories in dimension 2. David On 29 August 2010 19:31, Ronnie Brown <ronnie.profbrown@btinternet.com> wrote:
I would be grateful for information on published or available work in this area.
I am thinking of an additive category as a ring with several objects, as in Mitchell's well known paper. So in a sense am looking at 2-rings.
Thanks in anticipation.
Ronnie Brown
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Ronnie, only just saw your message via David's reply. Just for completeness it seems one should say that there is quite a bit known about additive n-categories even for n all the way from 1 to infinity -- they are called stable infinity-categories. Examples of these are in particular given by modules over infinity-rings -- which are maybe better known as ring spectra! A modern entry point into the theory, from a category-theoretic point of view is Jacob Lurie Commutative algebra http://arxiv.org/abs/math/0703204 But the basic elements and examples of the theory, such as E-infinity-rings, A-infinity-algebras and their modules and module categories are of course way older and quite classical even. All the best Urs On Mon, Aug 30, 2010 at 3:18 AM, David Roberts <droberts@maths.adelaide.edu.au> wrote:
Hi Ronnie,
There is the work of Matthieu Dupont, see his page
http://breckes.org/dom-en.html
His PhD thesis is on abelian categories in dimension 2.
David
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Ronnie, You can find many good things in Mathieu Dupont's PhD thesis: http://arxiv.org/abs/0809.1760 Richard On 29 August 2010 20:01, Ronnie Brown <ronnie.profbrown@btinternet.com>wrote:
I would be grateful for information on published or available work in this area.
I am thinking of an additive category as a ring with several objects, as in Mitchell's well known paper. So in a sense am looking at 2-rings.
Thanks in anticipation.
Ronnie Brown
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (4)
-
David Roberts -
Richard Garner -
Ronnie Brown -
Urs Schreiber