From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3930 Path: news.gmane.org!not-for-mail From: Joachim Kock Newsgroups: gmane.science.mathematics.categories Subject: Re: unital weak functor? Date: Fri, 21 Sep 2007 01:23:42 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7BIT X-Trace: ger.gmane.org 1241019611 10955 80.91.229.2 (29 Apr 2009 15:40:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Sep 21 14:21:16 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 Sep 2007 14:21:16 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IYm6y-00017J-54 for categories-list@mta.ca; Fri, 21 Sep 2007 14:16:16 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 54 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:3930 Archived-At: >Josh Nichols-Barrer wrote: > >>Is there a name for a weak functor between bicategories which takes >>identity 1-morphisms to identity 1-morphisms? The term 'normalised' (already mentioned in the replies) goes back at least to Grothendieck, SGA1, Exp VI: he calls a cleavage for a fibred category E -> B normalised if the cartesian lift of each identity arrow is an identity arrow -- this is exactly the condition for the correponding pseudo-functor B^op -> Cat to preserve identity arrows strictly. Joachim.