Limits in double categories, preprint

Limits in double categories, preprint

[categories]

Date: Wed, 12 Nov 1997 19:34:32 +0100
From: Marco Grandis <grandis@dima.unige.it>

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/