From: Marco Grandis <grandis@dima.unige.it>
To: categories@mta.ca
Subject: Adjoints for symmetric cubical categories (On weak cubical categories, III)
Date: Wed, 20 Feb 2013 11:00:48 +0100 [thread overview]
Message-ID: <E1U8Alj-0003mG-PH@mlist.mta.ca> (raw)
The following preprint is available
M. Grandis, Adjoints for symmetric cubical categories (On weak
cubical categories, III),
Dip. Mat. Univ. Genova, Preprint 601 (2013).
http://www.dima.unige.it/~grandis/CubAdj.pdf
Abstract. Extending a previous article (with R. Paré) on adjoints for
double categories, we deal here with weak symmetric cubical
categories (of infinite dimension). Also here, a general 'cubical
adjunction' has a colax cubical functor left adjoint to a lax one.
This cannot be viewed as an adjunction in some bicategory, because
composing lax and colax morphisms destroys all comparisons. However,
as in the case of double adjunctions, cubical adjunctions live in an
interesting double category; this now consists of weak symmetric
cubical categories, with lax and colax double functors as horizontal
and vertical arrows, linked by suitable double cells.
With best regards to colleagues and friends
Marco Grandis
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
reply other threads:[~2013-02-20 10:00 UTC|newest]
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