From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4392 Path: news.gmane.org!not-for-mail From: "Stephen Lack" Newsgroups: gmane.science.mathematics.categories Subject: RE: Further to my question on adjoints Date: Tue, 13 May 2008 08:38:30 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019916 13089 80.91.229.2 (29 Apr 2009 15:45:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:16 +0000 (UTC) To: "Categories list" Original-X-From: rrosebru@mta.ca Tue May 13 14:15:09 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2008 14:15:09 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Jvxv5-0006JF-Uq for categories-list@mta.ca; Tue, 13 May 2008 14:04:08 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 15 Original-Lines: 48 Xref: news.gmane.org gmane.science.mathematics.categories:4392 Archived-At: Dear Michael, I do not remember your original question, but here is an answer to this. Let C be Cat^op and E be the arrow category 2. It's easier to work in Cat itself. Then we are interested in the full subcategory consisting of all categories X which admit a presentation=20 I.2 --> J.2 --> X --> =20 where I and J are sets, and "." is cotensor: e.g. J.2 denotes the=20 coproduct of J copies of 2. But a category admits such a presentation if and only if it is free on=20 a graph, and the free categories are of course not closed under coequalizers. Steve. > -----Original Message----- > From: cat-dist@mta.ca [mailto:cat-dist@mta.ca] On Behalf Of=20 > Michael Barr > Sent: Monday, May 12, 2008 10:34 PM > To: Categories list > Subject: categories: Further to my question on adjoints >=20 > In March I asked a question on adjoints, to which I have=20 > received no correct response. Rather than ask it again, I=20 > will pose what seems to be a simpler and maybe more=20 > manageable question. Suppose C is a complete category and E=20 > is an object. Form the full subcategory of C whose objects=20 > are equalizers of two arrows between powers of E. Is that=20 > category closed in C under equalizers? (Not, to be clear,=20 > the somewhat different question whether it is internally complete.) >=20 > In that form, it seems almost impossible to believe that it=20 > is, but it is surprisingly hard to find an example. When E=20 > is injective, the result is relatively easy, but when I look=20 > at examples, it has turned out to be true for other reasons. =20 > Probably there is someone out there who already knows an example. >=20 > Michael >=20 >=20 >=20