From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/473 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: preprint available Date: Tue, 2 Sep 1997 09:19:15 -0300 (ADT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016987 25912 80.91.229.2 (29 Apr 2009 14:56:27 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:56:27 +0000 (UTC) To: categories Original-X-From: cat-dist Tue Sep 2 09:20:57 1997 Original-Received: by mailserv.mta.ca; id AA23716; Tue, 2 Sep 1997 09:19:15 -0300 Original-Lines: 39 Xref: news.gmane.org gmane.science.mathematics.categories:473 Archived-At: Date: Mon, 1 Sep 1997 14:47:02 +0200 (MET DST) From: Koslowski Dear Colleagues, An updated preprint of my paper "Beyond the Chu-construction", which I presented in Vancouver in July, is now available on my web-page http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/koslowski.html The abstract follows below. From a symmetric monoidal closed (= autonomous) category Po-Hsiang Chu originally constructed a *-autonomous one, ie, a self-dual autonomous category where the duality is realized by means of a dualizing object. Recently, Michael Barr introduced an extension for the non-symmetric, but closed, case that after an initial step utilized monads and modules between them. Since these tools are well-understood in a bicategorical setting, we introduce a notion of local *-autonomy for closed bicategories that turns out to be inherited by the bicategories of monads and the bicategory of interpolads. Since the first step of Barr's construction carries over directly to the bicategorical setting, we recover his main result as an easy corollary. Furthermore, the Chu-construction at this level may be viewed as a procedure to turn the endo-1-cells of a bicategory into the objects of a new bicategory, and hence is conceptually close to the constructions of bicategories of monads and of interpolads. Best regards, -- J"urgen -- J"urgen Koslowski % If I don't see you no more in this world ITI % I meet you in the next world TU Braunschweig % and don't be late! koslowj@iti.cs.tu-bs.de % Jimi Hendrix (Voodoo Child)