From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1910 Path: news.gmane.org!not-for-mail From: Michael Batanin Newsgroups: gmane.science.mathematics.categories Subject: Re: Looking for adjoints Date: Thu, 05 Apr 2001 12:59:11 +1000 Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018199 1141 80.91.229.2 (29 Apr 2009 15:16:39 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:16:39 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Fri Apr 6 15:43:45 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f36I5DV26188 for categories-list; Fri, 6 Apr 2001 15:05:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2022 In-Reply-To: Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:1910 Archived-At: This is just a small correction to Michael Barr message. The Kan's Ex^{\infty} is not a left adjoint to the inclusion of Kan simplicial sets into simplicial sets. In the original paper by Kan "On c.s.s. complexes" there is no mention about it being adjoint. Yet, the following is true Kan(Ex^{\infty}X,Y) is homotopy equivalent to Ssets(X,Y). So it is some sort of homotopy adjunction. Michael Batanin. >on 2/4/01 9:16 PM, Michael Barr at barr@barrs.org wrote: > The earliest that was labelled such was Kan's Ex^\infty, which was a left > adjoint to the inclusion of (what are now called) Kan simplicial sets into > simplicial sets. >