From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8020 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: P.J. Higgins' "Categories and Groupoids" question .... Date: Wed, 19 Feb 2014 13:08:07 +0000 Message-ID: References: Reply-To: Steve Vickers NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (1.0) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1392991945 972 80.91.229.3 (21 Feb 2014 14:12:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 21 Feb 2014 14:12:25 +0000 (UTC) Cc: Categories mailing list To: "Vasili I. Galchin" Original-X-From: majordomo@mlist.mta.ca Fri Feb 21 15:12:34 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 1WGqq5-0003JK-A0 for gsmc-categories@m.gmane.org; Fri, 21 Feb 2014 15:12:29 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:50971) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1WGqpD-0004U3-Sf; Fri, 21 Feb 2014 10:11:35 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1WGqpC-0005Z9-AZ for categories-list@mlist.mta.ca; Fri, 21 Feb 2014 10:11:34 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8020 Archived-At: Dear Vasili, I would say it is nothing to do with size issues, but stems from his stated a= im of treating categories as algebraic structures. If you look at the algebr= a of monoids, or of rings, you find that surjections are different from epis= . Examples: if you take a monoid and freely adjoin inverses, then you get an= epi from the first to the second that is not in general a surjection. The r= ing homomorphism from Z to Q is epi. Most algebraists would be more interest= ed in the surjections than the epis, and I think Higgins is just extending t= hat preference to particular categories such as C and G. Steve Vickers. > On 19 Feb 2014, at 07:29, "Vasili I. Galchin" wrote:= >=20 > Hello Cat Group, >=20 > I have been reading > http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html as well as > other works on groupoids .... I really like Higgins' book but in > Chapter 1 I keep seeing allusions to "injections" and > "surjections"instead of more general "monomorphisms" and > "epimorphisms", respectively. Is this because of his assumption (and > others ..) that starting point is a "small" graph, category, etc., > i.e. sets not classes? If so, has anybody expanded treatment of > groupoids beyond "sets" to "classes"? >=20 > Also IMO "subgraphs" should be presented as as "monos" in the > "graph category".... >=20 > Kind regards, >=20 > Vasili [For admin and other information see: http://www.mta.ca/~cat-dist/ ]