## Università degli Studi di Genova |

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 (which are generally non reversible) and a fundamental category (replacing the fundamental groupoid of the classical case). Finding a simple - possibly finite - model of the latter is a non-trivial problem, whose solution gives relevant information on the given 'space'; a problem which is of interest for applications as well as in general Category Theory. Here we continue the work "The shape of a category up to directed homotopy" [G3], with a deeper analysis of 'surjective models', motivated by studying the singularities of 3-dimensional ordered spaces. Keywords:homotopy theory, adjunctions, reflective subcategories, directed algebraic topology, MSC:55, 18 Pubblicato su: Theory and Applications of Categories Vol. 16 (2006) N. 26 Pag. 709-735 |