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
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