From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8642 Path: news.gmane.org!not-for-mail From: Uwe Egbert Wolter Newsgroups: gmane.science.mathematics.categories Subject: Categories with hyperedges? Date: Thu, 25 Jun 2015 14:34:36 +0200 Message-ID: Reply-To: Uwe Egbert Wolter NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1435339956 20275 80.91.229.3 (26 Jun 2015 17:32:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 26 Jun 2015 17:32:36 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Fri Jun 26 19:32:29 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.19]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Z8XUK-0000zL-Ks for gsmc-categories@m.gmane.org; Fri, 26 Jun 2015 19:32:28 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42537) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Z8XTG-00032J-HI; Fri, 26 Jun 2015 14:31:22 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Z8XTH-0002iI-9Q for categories-list@mlist.mta.ca; Fri, 26 Jun 2015 14:31:23 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8642 Archived-At: Dear all, Categories can be defined by extending directed multi graphs with identities and composition. The underlying directed multi graph of a small category C is given by the sets C_Mor, C_Obj and the source and target maps src^C,trg^C:C_Mor -> C_Obj. Has it ever been investigated what structures arise when we try, instead, to extend directed multi hypergraphs by identities and composition? A "directed multi hypergraph" H is thereby given by a set H_E of edges, a set H_V of vertices and two maps src^H,trg^H:H_E -> Pow(H_V) from H_E into the power set Pow(H_V) of H_V. I'm aware of monoidal categories and I would like to know if there is something else around. Any comment or reference is welcome Uwe Wolter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]