From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9240 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Functors arising from a relational Grothendieck construction Date: Fri, 16 Jun 2017 15:16:57 +0200 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1497624925 20113 195.159.176.226 (16 Jun 2017 14:55:25 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 16 Jun 2017 14:55:25 +0000 (UTC) Cc: categories@mta.ca To: Luc Pellissier Original-X-From: majordomo@mlist.mta.ca Fri Jun 16 16:55:19 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dLsec-0004hL-2G for gsmc-categories@m.gmane.org; Fri, 16 Jun 2017 16:55:18 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:33926) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dLseu-0007v2-6g; Fri, 16 Jun 2017 11:55:36 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dLsdj-0008PH-SL for categories-list@mlist.mta.ca; Fri, 16 Jun 2017 11:54:23 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9240 Archived-At: Dear Luc, by a theorem of B'enabou (and R. Street independently I guess) functors to BB correspond to lax normalized functors from BB^op to Dist, the bicategory of distributors. (see e.g. "Distributors at Work" on my homepage). This equivalence restricts to one between Conduch'e fibrations over BB and normalized pseudofunctors from BB^op to Dist. Replacing Set by 2 (i.e. {\emptyset,{\emptyset}}) and restricting to discrete guys functors from BB^op to Rel are equivalent to Conduch'e fibrations over BB which are faithful and reflect identities. In this case the Conduch'e condition amounts to a unique lifting property of factorization from the base tot he total category. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]