The following preprint is available. It is a sequel of my previous work on the fundamental category of a directed space, announced on this list in May 2004. M. Grandis Modelling fundamental 2-categories for directed homotopy Dip. Mat. Univ. Genova, Preprint 527 (2005), 34 p. Abstract. Directed Algebraic Topology is a recent field, deeply linked with ordinary and higher dimensional Category Theory. A 'directed space', e.g. an ordered topological space, has directed homotopies (generally non reversible) and fundamental n-categories (replacing the fundamental n-groupoids of the classical case). Finding a simple model of the latter is a non-trivial problem, whose solution gives relevant information on the given 'space'; a problem which is also of interest in general Category Theory, as it requires equivalence relations wider than categorical equivalence. Taking on a previous work on "The shape of a category up to directed homotopy", we study now the fundamental 2-category of a directed space. All the notions of 2-category theory used here are explicitly reviewed. http://www.dima.unige.it/~grandis/Shp2.pdf http://www.dima.unige.it/~grandis/Shp2.ps ________________ The first paper, "The shape of a category up to directed homotopy", can also be downloaded: Abstract: http://www.dima.unige.it/~grandis/Shp.Abs.html Paper: http://www.dima.unige.it/~grandis/Shp.pdf http://www.dima.unige.it/~grandis/Shp.ps ________________ 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/ 24-Mar-2005 13:53:44 -0400,6340;000000000001-00000000