From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8557 Path: news.gmane.org!not-for-mail From: Giorgio Mossa Newsgroups: gmane.science.mathematics.categories Subject: Re: Partial functor Date: Mon, 16 Mar 2015 16:29:22 +0100 Message-ID: References: Reply-To: Giorgio Mossa NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1426590937 17679 80.91.229.3 (17 Mar 2015 11:15:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 17 Mar 2015 11:15:37 +0000 (UTC) Cc: categories@mta.ca To: Christopher King Original-X-From: majordomo@mlist.mta.ca Tue Mar 17 12:15:29 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 1YXpT1-0003I7-Rv for gsmc-categories@m.gmane.org; Tue, 17 Mar 2015 12:15:24 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42385) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YXpS6-0007Sr-G7; Tue, 17 Mar 2015 08:14:26 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YXpS5-0003kQ-1U for categories-list@mlist.mta.ca; Tue, 17 Mar 2015 08:14:25 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8557 Archived-At: On Sun, Mar 15, 2015 at 05:01:58PM +0000, Christopher King wrote: > David Leduc googlemail.com> writes: > >> >> Hi, >> >> 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. >> >> [For admin and other information see: http://www.mta.ca/~cat-dist/ ] >> >> > > I know this is late, but I find a quite obvious notion for it. Why not turn > your partial functor into a regular functor from C->D+1 (1 and + are the > terminal object and coproduct in the category of categories.) Now you can just > use regular natural transformations. > If your idea is to mimic the construction used for modelling partial function as (total) function in Kleisli category for the monad (- ??? 1) in Set then this does not work in Cat. The reason is that a functor P : C ??? D ??? 1 in order to correspond to a partial functor P' : S ??? C ??? D should send the category S in D and al the other stuff in 1, nonetheless is ?? : s ??? c is a morphism from an object of S to an object in C ??? S there is no way to map ?? in a morphism in D ??? 1 (= D + 1 in your notation), because the two subcategories D and 1 in D ??? 1 are disjoint/disconnected and s should be mapped in D while c should be mapped in 1. Best regards Giorgio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]