From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6920 Path: news.gmane.org!not-for-mail From: Emily Riehl Newsgroups: gmane.science.mathematics.categories Subject: partial categories Date: Wed, 28 Sep 2011 16:34:30 -0400 (EDT) Message-ID: Reply-To: Emily Riehl NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1317249659 10601 80.91.229.12 (28 Sep 2011 22:40:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 28 Sep 2011 22:40:59 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Thu Sep 29 00:40:55 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R92oA-0001QB-Vw for gsmc-categories@m.gmane.org; Thu, 29 Sep 2011 00:40:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40374) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R92ml-0004R5-6P; Wed, 28 Sep 2011 19:39:27 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R92mj-0001a9-J1 for categories-list@mlist.mta.ca; Wed, 28 Sep 2011 19:39:25 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6920 Archived-At: A colleague of mine is wondering if anyone has studied "partial categories," by which she means directed graphs with identities but with only some compositions (including all identity compositions) defined. A partial category can be thought of as a category enriched in pointed sets (with smash product as tensor and S^0 as unit). The slogan is that the basepoint in each hom-set stands in for "does not exist". But enriched functors don't give the right notion of maps; these should preserve identities and all specified compositions. Enriched functors behave appropriately with regards to the identites but may "forget" extant arrows and in particular need not preserve composites. So perhaps this perspective is not useful. I'll happily pass along any suggestions. Thanks, Emily Riehl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]