Subject: categories: Preprint: The shape of a category up to directed homotopy

From: Marco Grandis <[email-masked]>
Date: Thu, 20 May 2004 15:03:12 +0200

The following preprint is available:

M. Grandis,
The shape of a category up to directed homotopy,
Dip. Mat. Univ. Genova, Preprint 509 (May 2004), 44 p.

Abstract.  This work is a contribution to a recent field, Directed
Algebraic Topology. Categories which appear as fundamental categories of
'directed structures', e.g. ordered topological spaces, have to be studied
up to appropriate notions of directed homotopy equivalence, wider than
ordinary equivalence of categories.

   Here we introduce 'past' and 'future equivalences' of categories - sort
of symmetric versions of an adjunction - and use them and their
combinations to get 'directed models' of a category; in the simplest case,
these are the join of the least full reflective and the least full
coreflective subcategory.

MSC: 55Pxx, 18A40, 68Q85.

Keywords: homotopy theory, adjunctions, reflective subcategories, directed
algebraic topology, fundamental category, concurrent processes .

Available as pdf or ps:

http://www.dima.unige.it/~grandis/Shp.pdf
http://www.dima.unige.it/~grandis/Shp.ps

With best regards

     Marco Grandis

Dipartimento di Matematica
Universita` di Genova
via Dodecaneso 35
16146 GENOVA, Italy

e-mail: [email-masked]
tel: +39.010.353 6805   fax: +39.010.353 6752
http://www.dima.unige.it/~grandis/