* Preprint: Adjoints for double categories
@ 2003-02-28 10:29 Marco Grandis
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From: Marco Grandis @ 2003-02-28 10:29 UTC (permalink / raw)
To: categories
The following preprint is available, in ps:
M. Grandis - R. Pare´
Adjoints for double categories
Dip. Mat. Univ. Genova, Preprint 476 (2003), 40 p.
http://www.dima.unige.it/~grandis/Dbl.Adj.ps
Abstract. After 'Limits in double categories' (Cahiers Topologie Geom.
Differentielle Categ. 40 (1999), 162-220), we pursue our study of the
general theory of weak double categories, addressing adjunctions and
monads. A general 'double adjunction', which appears often in concrete
constructions, has a *colax* double functor left adjoint to a *lax* one.
This cannot be viewed as an adjunction in some bicategory, because lax and
colax morphisms do not compose well and do not form one. However, such
adjunctions live within an interesting construct, the strict double
category of weak double categories, with horizontal and vertical arrows
provided by the lax and colax double functors, respectively, and a suitable
notion of double cell.
Marco Grandis
Dipartimento di Matematica
Universita` di Genova
via Dodecaneso 35
16146 GENOVA, Italy
e-mail: grandis@dima.unige.it
tel: +39.010.353 6805 fax: +39.010.353 6752
http://www.dima.unige.it/~grandis/
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