Preprint: Absolute lax 2-categories

[Marco Grandis <grandis@dima.unige.it>]

The preprint described below is available, in pdf.

I would like to have information on other works considering *absolute*
comparison cells/constraints, in weak or lax structures.

Best wishes to all colleagues and friends

Marco Grandis

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M. Grandis,
Absolute lax 2-categories
Dip. Mat. Univ. Genova, Preprint 533 (2005), 22 p.

 http://www.dima.unige.it/~grandis/LCat2.pdf

Abstract.

   We have introduced, in a previous paper, the fundamental lax 2-category
of a 'directed space' X. Here we show that, when X has a T1-topology, this
structure can be embedded into a larger one, with the same objects (the
points of X), the same arrows (the directed paths) and the same cells
(based on directed homotopies of paths), but a larger system of comparison
cells.

   The new comparison cells are *absolute*, in the sense that they only
depend on the arrows themselves rather than on their syntactic expression,
as in the usual settings of lax or weak structures. It follows that, in the
original structure, all the diagrams of comparison cells commute, even if
not constructed in a natural way and even if the composed cells need not
stay within the old system.
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The previous preprint mentioned above ('Lax 2-categories and directed
homotopy') is also available, at:

http://www.dima.unige.it/~grandis/LCat.pdf

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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/