From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7046 Path: news.gmane.org!not-for-mail From: Steve Lack Newsgroups: gmane.science.mathematics.categories Subject: Re: Partial functor Date: Fri, 11 Nov 2011 11:10:41 +1100 Message-ID: References: Reply-To: Steve Lack NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1084) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1321020051 18029 80.91.229.12 (11 Nov 2011 14:00:51 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 11 Nov 2011 14:00:51 +0000 (UTC) Cc: categories To: David Leduc Original-X-From: majordomo@mlist.mta.ca Fri Nov 11 15:00:46 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ROrew-0006ml-39 for gsmc-categories@m.gmane.org; Fri, 11 Nov 2011 15:00:46 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:56438) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1ROrdC-00069U-3M; Fri, 11 Nov 2011 09:58:58 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ROrdA-0002L0-Iv for categories-list@mlist.mta.ca; Fri, 11 Nov 2011 09:58:56 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7046 Archived-At: Dear David, There are many possible meanings of partial morphism between categories, depending on what meaning you attach to "subcategory". Different = meanings will be appropriate depending on the applications in question. One possibility, which I believe was first considered by Lawvere, is to = take "subcategory"=20 of C to be a discrete opfibration over C. The resulting 2-category is = described in=20 detail in the appendix of=20 Stephen Lack and Ross Street, The formal theory of monads II, JPAA = 175:243-265, 2002. where it is also shown that these partial maps are classified, in a = suitable sense, by the Fam construction.=20 Regards, Steve Lack. On 07/11/2011, at 11:55 PM, david leduc wrote: > Hi, >=20 > A partial functor from C to D is given by a subcategory S of C and a > functor from S to D. What is the appropriate notion of natural > transformation between partial functors that would allow to turn small > categories, partial functors and those "natural transformations" into > a bicategory? The difficulty is that two partial functors from C to D > might not have the same definition domain. >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]