From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1113 Path: news.gmane.org!not-for-mail From: Reiko Heckel Newsgroups: gmane.science.mathematics.categories Subject: Kleisli bi-categories Date: Wed, 05 May 1999 10:22:24 +0200 Organization: Uni Paderborn Message-ID: <372FFFC0.60201EB2@uni-paderborn.de> 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 1241017575 29561 80.91.229.2 (29 Apr 2009 15:06:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:06:15 +0000 (UTC) To: Categories Mailing List Original-X-From: cat-dist Thu May 6 23:29:26 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id WAA07955 for categories-list; Thu, 6 May 1999 22:48:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.51 [en] (X11; I; SunOS 5.6 sun4u) X-Accept-Language: de-DE, en Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 36 Xref: news.gmane.org gmane.science.mathematics.categories:1113 Archived-At: Dear Category Theorists, I'm looking for a reference on the following bi-categorical variant of the construction of Kleisli categories. Start from a pseudo-free construction $F$ between (2-)categories $\cat C$ and $\cat D$. In the case I'm interested in, $F$ arises from a finite cocompletion. For example, $\cat C$ is the category of small categories and $\cat D$ is the category of small categories with finite colimits. Constructing (in the usual way) the Kleisli category $\cat K$ for $F$ leads to a bi-category since the universal property used to define the composition in $\cat K$ holds only up to a unique natural isomorphism. Then, there exists a (unique?) homomorphism of bi-categories $G: \cat K \to \cat D$ which commutes with the obvious embedding of $\cat C$ into $\cat K$ and (the pseudo functor induced by) $F$. I understand that pseudo-free constructions of the above kind can be axiomatized by means of Kock-Zoeberlein (KZ) monads. Thus, any reference on Kleisli-like constructions for KZ monads would do. For me, it was simpler to work directly with the universal properties, in particular since all the coherence laws are automatic. Any hints or references to relevant literature would be much appreciated. Best regards, Reiko Heckel. -- Reiko Heckel E-Mail:reiko@uni-paderborn.de Univ. GH Paderborn, FB 17 Tel: ++49-05251-60-3356 Warburger Str. 100, E4.130 Fax: ++49-05251-60-3431 33098 Paderborn, Germany