From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/526 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Limits in double categories, preprint Date: Thu, 13 Nov 1997 15:56:57 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017016 26122 80.91.229.2 (29 Apr 2009 14:56:56 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:56:56 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Nov 13 15:58:28 1997 Original-Received: by mailserv.mta.ca; id AA14329; Thu, 13 Nov 1997 15:56:57 -0400 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:526 Archived-At: Date: Wed, 12 Nov 1997 19:34:32 +0100 From: Marco Grandis The following preprint is available: Limits in double categories by Marco Grandis and Robert Pare Abstract. We define the notion of (horizontal) double limit for a double functor F: I -> A between double categories, and we give a construction theorem for such limits, from double products, double equalisers and tabulators (the double limits of vertical arrows). Double limits can describe important tools; for instance, the Grothendieck construction of a profunctor is its tabulator, in the "double category" of categories, functors and profunctors. If A is a 2-category, the previous result reduces to Street's construction theorem of weighted limits, by ordinary limits and cotensors 2*X (the tabulator of the vertical identity of the object X). Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.10.353 6805 fax: +39.10.353 6752 home page: http://www.dima.unige.it/STAFF/GRANDIS/