additive 2-categories and related structures?

additive 2-categories and related structures?

[Ronnie Brown]

   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


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Re: additive 2-categories and related structures?

[David Roberts]

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/ ]

Re: additive 2-categories and related structures?

[Richard Garner]

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/ ]

Re: additive 2-categories and related structures?

[Urs Schreiber]

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/ ]