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/ ]