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From: Fernando Muro <fmuro@ub.edu>
To: Hasse Riemann <rafaelb77@hotmail.com>, <categories@mta.ca>
Subject: Re: What is classified by cohomology?
Date: Thu, 21 May 2009 20:04:23 +0200	[thread overview]
Message-ID: <E1M7URk-0003iS-OY@mailserv.mta.ca> (raw)

Dear Hasse,

> What does the cohomology H^n(X;coefficients) classify, for X a more general
> object then a group and especially when X is a category?
> I know that the case X=group gives n-torsors.

Group cohomology also classifies crossed extensions:

Huebschmann, Johannes
Crossed $n$-fold extensions of groups and cohomology.
Comment. Math. Helv. 55 (1980), no. 2, 302--313. 

There is a similar approach for cohomology of categories in:

Baues, Hans-Joachim(D-MPI); Minian, Elias Gabriel(D-MPI)
Track extensions of categories and cohomology. (English summary)
$K$-Theory 23 (2001), no. 1, 1--13. 

The cases n = 0, 1, 2, 3 were known before, see references therein.

Best,

Fernando

-- 
Fernando Muro
Universitat de Barcelona, Departament d'Àlgebra i Geometria
http://atlas.mat.ub.es/personals/muro/





             reply	other threads:[~2009-05-21 18:04 UTC|newest]

Thread overview: 2+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2009-05-21 18:04 Fernando Muro [this message]
  -- strict thread matches above, loose matches on Subject: below --
2009-05-20 23:09 Hasse Riemann

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