From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8567 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Partial functors .. Date: Wed, 18 Mar 2015 11:47:18 +1100 Message-ID: References: Reply-To: Ross Street NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Mac OS X Mail 7.3 \(1878.6\)) Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1426681710 21843 80.91.229.3 (18 Mar 2015 12:28:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 18 Mar 2015 12:28:30 +0000 (UTC) Cc: Categories list To: David Yetter Original-X-From: majordomo@mlist.mta.ca Wed Mar 18 13:28:23 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YYD59-0007ko-Cn for gsmc-categories@m.gmane.org; Wed, 18 Mar 2015 13:28:19 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:44020) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YYD4T-0003dJ-AQ; Wed, 18 Mar 2015 09:27:37 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YYD4R-0006Pr-OA for categories-list@mlist.mta.ca; Wed, 18 Mar 2015 09:27:35 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8567 Archived-At: Dear All David Leduc=92s statement:=20 "A partial functor from C to D is given by a subcategory S of C and a = functor from S to D.=94 If this is taken as given then today I don=92t want to add to what = people have said. But there is another notion of partial functor that I learnt from Brian = Day who learnt it from Bill Lawvere. If we are to replace 2 in Set by Set in = Cat, then characteristic maps C =97> 2 should become presheaves C^op =97> = Set, so injective functions S=97> C should become discrete fibrations E =97> = C. Then a partial map from C to D would be a span C <=97 E =97> D with C <=97 E a discrete fibration and E =97> D any functor. The partial map classifier is then the coproduct completion FamD of D. Add size restrictions, to taste. Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]