From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8784 Path: news.gmane.org!not-for-mail From: Paul B Levy Newsgroups: gmane.science.mathematics.categories Subject: two categories of interest Date: Thu, 7 Jan 2016 15:09:38 +0000 Message-ID: Reply-To: Paul B Levy NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1452181820 4954 80.91.229.3 (7 Jan 2016 15:50:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 7 Jan 2016 15:50:20 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Thu Jan 07 16:50:12 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.22]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1aHCpH-0004C7-4F for gsmc-categories@m.gmane.org; Thu, 07 Jan 2016 16:50:11 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:56927) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1aHCoT-0000cw-03; Thu, 07 Jan 2016 11:49:21 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1aHCoO-0001V2-Vi for categories-list@mlist.mta.ca; Thu, 07 Jan 2016 11:49:16 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8784 Archived-At: Dear all, Have either of the following categories been studied before? 1. A "set with loners" is a set A with a subset U, whose elements are called "loners". A "loner-respecting function" (A,U) --> (B,V) is a function A --> B such that for any x in U, f(x) is in V and its only f-preimage is x. Let SWL be the category of sets with loners and loner-respecting functions, and Inj the category of sets and injections. Both Set and Inj are isomorphic to full subcategories of SWL. 2. For sets A and B, a "sum preorder" from A to B is a preorder on A+B. Example: A is the set of men, B is the set of women, take the preorder "younger than or the same age as". An equivalence relation on A+B is called a "corelation" from A to B. Given sum preorders R : A --> B and S : B --> C, obtain the composite by taking the least preorder on A+B+C that contains R and S, and then restricting to A+C. Let SumPreord be the category of sets and sum preorders, Rel the category of sets and relations, and Corel the category of sets and corelations. Both Rel and Corel are isomorphic to lluf subcategories of SumPreord. Paul -- Paul Blain Levy School of Computer Science, University of Birmingham http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]