From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/963 Path: news.gmane.org!not-for-mail From: Mamuka Jibladze Newsgroups: gmane.science.mathematics.categories Subject: Re: one-object closed categories Date: Sat, 12 Dec 1998 23:31:20 +0200 (EET) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017391 28579 80.91.229.2 (29 Apr 2009 15:03:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:03:11 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Sun Dec 13 16:17:07 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id PAA09421 for categories-list; Sun, 13 Dec 1998 15:15:50 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:963 Archived-At: Concerning categories enriched in monoidal categories with a single object: another example is given by cocycles. It can be presented in various ways. For example, a "\v Cech style" version: given an open cover of X by Ui and a (suitably normalized) \v Cech 3-cocycle c of this cover with values in M, this enrichs in the evident way the category whose objects are the i's, with hom(i,j) either a singleton or empty according to inhabitedness of the intersection of Ui and Uj. Other variations suggest things like morphisms of simplicial sets to the nerve of M considered as a 2-category with a single 1-cell. This is related to K(M,2)-torsors, etc. Quite probably there are several publications exploiting this. At least cocycles with values in monoids rather than groups certainly have been considered. What I certainly have not seen is a backwards generalization: has anybody considered analogs of K(M,2)-torsors for general enrichments? Would be very interested in a reference. Happy holidays to all! Mamuka