From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8198 Path: news.gmane.org!not-for-mail From: Pawel Sobocinski Newsgroups: gmane.science.mathematics.categories Subject: Re: Limits in REL Date: Sun, 6 Jul 2014 23:43:56 +0100 Message-ID: References: Reply-To: Pawel Sobocinski NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1404723920 27872 80.91.229.3 (7 Jul 2014 09:05:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 7 Jul 2014 09:05:20 +0000 (UTC) Cc: "categories@mta.ca" To: Ondrej Rypacek Original-X-From: majordomo@mlist.mta.ca Mon Jul 07 11:05:13 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1X44rE-0004HF-Bw for gsmc-categories@m.gmane.org; Mon, 07 Jul 2014 11:05:08 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45136) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1X44qt-0003wd-DR; Mon, 07 Jul 2014 06:04:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1X44qr-0005xh-Co for categories-list@mlist.mta.ca; Mon, 07 Jul 2014 06:04:45 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8198 Archived-At: Dear Ondrej, Since many people have already replied to you about Rel, let me add something about colimits in Span(C). Note that since Span(C) is a bicategory, the "morally correct" notion is bicolimits. With Tobias Heindel we showed that any colimit diagram in C that satisfies something called a Van Kampen property is mapped to a bicolimit diagram through the canonical embedding C -> Span(C). So the Van Kampen property is really a characterisation of when a colimit satisfies the universal property of being a (bi)colimit in the wild world of Span(C). Some examples of Van Kampen properties for particular colimits: a Van Kampen initial object is a strict initial object, a Van Kampen coproduct is a coproduct that has the properties of coproducts in extensive categories, a Van Kampen pushout is a pushout that has the properties of pushouts (along monos) in adhesive categories. You will find the details and more examples in: Tobias Heindel, Pawel Sobocinski: Being Van Kampen is a universal property. Logical Methods in Computer Science 7(1) (2011) All the best, Pawel. On 3 July 2014 11:57, Ondrej Rypacek wrote: > Hi all > > What is known about limits in REL , the (bi)category of sets and relations? > I know there are biproducts; are there equalisers? > > And what about SPAN(C) or REL(C), spans and relations over a suitable > category C ? > > Thanks a lot in advance, > Ondrej > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]