Geodesic
Quotient models of a category up to directed homotopy
Theory and applications of categories, Tome 16 (2006), pp. 709-735.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 55Pxx, 18A40, 68Q85
Keywords: homotopy theory, adjunctions, reflective subcategories, directed algebraic topology, fundamental category, concurrent processes 
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     author = {Marco Grandis},
     title = {Quotient models of a category up to directed homotopy},
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     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a25/}
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Marco Grandis. Quotient models of a category up to directed homotopy. Theory and applications of categories, Tome 16 (2006), pp. 709-735. http://geodesic.mathdoc.fr/item/TAC_2006_16_a25/