From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4880 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: sketch theory Date: Sun, 24 May 2009 22:03:44 -0700 Message-ID: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1243265819 10331 80.91.229.12 (25 May 2009 15:36:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 25 May 2009 15:36:59 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Mon May 25 17:36:52 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1M8cEM-0000YU-MV for gsmc-categories@m.gmane.org; Mon, 25 May 2009 17:36:50 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M8bdo-0005Nc-RU for categories-list@mta.ca; Mon, 25 May 2009 11:59:04 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4880 Archived-At: Steve Lack writes: You ask about a sketch for cartesian closed categories. Have a look at > at the paper "A presentation of topoi as algebraic relative to categories > or > graphs (Dubuc-Kelly, J. Alg. 81: 420-433, 1983). This describes something > even tighter: the category of cartesian closed categories is monadic over > the category of graphs. > Thanks! And thanks to everyone else for their helpful comments. I'm behind on answering my emails. In this approach, does each pair of objects in a ccc come with a chosen product and exponential? Are the morphisms of ccc's are required to preserve these on the nose? At first I was a bit shocked to hear of a sketch for ccc's, because the internal hom is contravariant in one variable. But I guess that as long as we treat ccc's purely 1-categorically that's no problem. But then I guess we pay the price of "undue strictness". Right? Best, jb