From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6927 Path: news.gmane.org!not-for-mail From: =?windows-1252?Q?Lutz_Schr=F6der?= Newsgroups: gmane.science.mathematics.categories Subject: Re: partial categories Date: Thu, 29 Sep 2011 14:24:27 +0200 Message-ID: References: Reply-To: =?windows-1252?Q?Lutz_Schr=F6der?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1317300001 19765 80.91.229.12 (29 Sep 2011 12:40:01 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 29 Sep 2011 12:40:01 +0000 (UTC) To: Emily Riehl , categories Original-X-From: majordomo@mlist.mta.ca Thu Sep 29 14:39:56 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 1R9Fu3-0007Iu-W8 for gsmc-categories@m.gmane.org; Thu, 29 Sep 2011 14:39:52 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:34918) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R9Fsa-0002zX-Ma; Thu, 29 Sep 2011 09:38:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R9FsZ-0004RA-3c for categories-list@mlist.mta.ca; Thu, 29 Sep 2011 09:38:19 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6927 Archived-At: I studied these things in my PhD work. The thesis itself is in German,=20 I'm afraid, but there's a series of papers based on it which you can=20 find on my homepage. Maybe the most interesting one for you might be the=20 paper with Mateus on probabilistic automata (which form a certain type=20 of partial category) in MSCS 12 (2002), pp. 481=96512. Regards, Lutz Am 28.09.2011 22:34, schrieb Emily Riehl: > A colleague of mine is wondering if anyone has studied "partial > categories," by which she means directed graphs with identities but wit= h > 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 enric= hed > 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 > --=20 -------------------------------------- Prof. Dr. Lutz Schr=F6der Senior Researcher DFKI Bremen=09 Safe and Secure Cognitive Systems Cartesium, Enrique-Schmidt-Str. 5 D-28359 Bremen phone: (+49) 421-218-64216 Fax: (+49) 421-218-9864216 mail: Lutz.Schroeder@dfki.de www.dfki.de/sks/staff/lschrode -------------------------------------- ------------------------------------------------------------- Deutsches Forschungszentrum f=FCr K=FCnstliche Intelligenz GmbH Firmensitz: Trippstadter Strasse 122, D-67663 Kaiserslautern Gesch=E4ftsf=FChrung: Prof. Dr. Dr. h.c. mult. Wolfgang Wahlster (Vorsitzender) Dr. Walter Olthoff Vorsitzender des Aufsichtsrats: Prof. Dr. h.c. Hans A. Aukes Amtsgericht Kaiserslautern, HRB 2313 ------------------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]