From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/135 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Bi-presheaves Date: Sat, 7 Mar 2009 17:15:29 +1100 Message-ID: Reply-To: Ross Street NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1236471140 5553 80.91.229.12 (8 Mar 2009 00:12:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 8 Mar 2009 00:12:20 +0000 (UTC) To: Andrew Stacey , categories Original-X-From: categories@mta.ca Sun Mar 08 01:13:37 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 1Lg6e6-0003zk-C9 for gsmc-categories@m.gmane.org; Sun, 08 Mar 2009 01:13:34 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Lg66J-0002UT-8e for categories-list@mta.ca; Sat, 07 Mar 2009 19:38:39 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:135 Archived-At: Given a category A, the Isbell envelope E(A) is the category whose objects are triplets (F_*, F^*, t) where F_* : A --> Set and F^* : A^{op} --> Set are functors and t_{a,b} : F^*(a) x F_*(b) --> A(a,b) is a family natural in a and b in A. The morphisms are as you described. There is a "double Yoneda" A --> E(A) taking c to (A(c,-), A(-,c), composition). ==Ross On 06/03/2009, at 7:19 PM, Andrew Stacey wrote: > When you say that you call it 'the Isbell envelope', what do you > mean? Is the > category the 'Isbell envelope of/on the original category' or are > the objects > 'Isbell envelopes' and we have the category of Isbell envelopes (in/ > on/of the > original category)?