From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/124 Path: news.gmane.org!not-for-mail From: Andrew Stacey Newsgroups: gmane.science.mathematics.categories Subject: Bi-presheaves Date: Thu, 5 Mar 2009 16:34:46 +0100 Message-ID: Reply-To: Andrew Stacey NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1236307326 27616 80.91.229.12 (6 Mar 2009 02:42:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 6 Mar 2009 02:42:06 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Fri Mar 06 03:43:24 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 1LfQ1x-00070O-V9 for gsmc-categories@m.gmane.org; Fri, 06 Mar 2009 03:43:22 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LfPPq-0002YJ-1S for categories-list@mta.ca; Thu, 05 Mar 2009 22:03:58 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:124 Archived-At: Dear Categorists, I'm interested in looking at the following type of thing: Start with an essentially small category, T, and look at the category whose objects are triples (P,F,c) where: P is a contravariant functor T -> Set, F is a covariant functor T -> Set and c is a natural transformation from P x F to the Hom bi-functor. Morphisms are pairs of natural transformations P_1 -> P_2 and F_2 -> F_1 that intertwine the natural transformations c_1 and c_2. One could also enrich the whole structure. Has this cropped up anywhere before? If so, what is it called and where can I learn about it? If not, what shall I call it? If this is something standard then please pardon my ignorance. I'm fairly new to _real_ category theory and am still just learning the basics. Thanks, Andrew Stacey