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/
next 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
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1M7URk-0003iS-OY@mailserv.mta.ca \
--to=fmuro@ub.edu \
--cc=categories@mta.ca \
--cc=rafaelb77@hotmail.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).