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", 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, fundamental category, concurrent processes
2000 MSC: 55Pxx, 18A40, 68Q85
Theory and Applications of Categories,
Vol. 16, 2006,
No. 26, pp 709-735.