From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8230 Path: news.gmane.org!not-for-mail From: Adam Gal Newsgroups: gmane.science.mathematics.categories Subject: Final objects in 2-categories Date: Thu, 24 Jul 2014 16:52:02 +0200 Message-ID: Reply-To: Adam Gal NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1406244434 6841 80.91.229.3 (24 Jul 2014 23:27:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 24 Jul 2014 23:27:14 +0000 (UTC) To: Categories mailing list Original-X-From: majordomo@mlist.mta.ca Fri Jul 25 01:27:09 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XASPi-0001tQ-Mz for gsmc-categories@m.gmane.org; Fri, 25 Jul 2014 01:27:06 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48126) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XASPC-0006el-7T; Thu, 24 Jul 2014 20:26:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XASPC-00035j-6O for categories-list@mlist.mta.ca; Thu, 24 Jul 2014 20:26:34 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8230 Archived-At: Hi all, Has someone studied the notion of final objects in a 2-category? I know that we can define it using the classifying space, and that in this sense Quillen's theorem A holds and tells us this is equivalent to some fibers being contractible. This seems to be a bit too coarse though. For instance in our recent paper (with E. Gal) we wanted to prove that something is final, and what we showed is that these fibers have an initial and final object. So they definitely have contractible classifying spaces, but it seems that we can say something more precise than this. The question is if this fits into some finer notion of final object in 2-categories which has been studied. Thanks, Adam [For admin and other information see: http://www.mta.ca/~cat-dist/ ]