From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4862 Path: news.gmane.org!not-for-mail From: Fernando Muro Newsgroups: gmane.science.mathematics.categories Subject: Re: What is classified by cohomology? Date: Thu, 21 May 2009 20:04:23 +0200 Message-ID: Reply-To: Fernando Muro NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1243000077 18283 80.91.229.12 (22 May 2009 13:47:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 22 May 2009 13:47:57 +0000 (UTC) To: Hasse Riemann , Original-X-From: categories@mta.ca Fri May 22 15:47:49 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1M7V6D-000389-Mm for gsmc-categories@m.gmane.org; Fri, 22 May 2009 15:47:49 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M7URk-0003iS-OY for categories-list@mta.ca; Fri, 22 May 2009 10:06:00 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4862 Archived-At: Dear Hasse, > What does the cohomology H^n(X;coefficients) classify, for X a more gen= eral > object then a group and especially when X is a category? > I know that the case X=3Dgroup 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.=20 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.=20 The cases n =3D 0, 1, 2, 3 were known before, see references therein. Best, Fernando --=20 Fernando Muro Universitat de Barcelona, Departament d'=C0lgebra i Geometria http://atlas.mat.ub.es/personals/muro/