From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8571 Path: news.gmane.org!not-for-mail From: Steve Lack Newsgroups: gmane.science.mathematics.categories Subject: Re: Partial functors .. Date: Thu, 19 Mar 2015 08:36:33 +1100 Message-ID: References: Reply-To: Steve Lack NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Mac OS X Mail 8.2 \(2070.6\)) Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1426722917 16329 80.91.229.3 (18 Mar 2015 23:55:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 18 Mar 2015 23:55:17 +0000 (UTC) Cc: David Yetter , Categories list To: Ross Street Original-X-From: majordomo@mlist.mta.ca Thu Mar 19 00:55:10 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 1YYNnq-0006LI-8t for gsmc-categories@m.gmane.org; Thu, 19 Mar 2015 00:55:10 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:46108) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YYNnG-0007CI-Hz; Wed, 18 Mar 2015 20:54:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YYNn8-00055s-SA for categories-list@mlist.mta.ca; Wed, 18 Mar 2015 20:54:26 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8571 Archived-At: Dear Ross, I think you meant the *product* completion Fam(D*)*.=20 If you use the coproduct completion, then you need to use discrete = *opfibrations* and covariant Set-valued functors. There are some details in the appendix to our joint paper =93The formal = theory of monads II=94. Steve. > On 18 Mar 2015, at 11:47 am, Ross Street = wrote: >=20 > Dear All >=20 > 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 >=20 > If this is taken as given then today I don=92t want to add to what = people have said. >=20 > 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. >=20 > Ross >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]