Geodesic
Modelling fundamental 2-categories for directed homotopy
Homology, homotopy, and applications, Tome 8 (2006) no. 1, pp. 31-70.

Voir la notice de l'article provenant de la source International Press of Boston

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 fundamental n-categories (replacing the fundamental $n$-groupoids of the classical case). Finding a simple model of the latter is a nontrivial 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 which are more general 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.
DOI : 10.4310/HHA.2006.v8.n1.a2
Classification : 18A40, 18D05, 55Pxx, 55Qxx, 55Uxx
Keywords: 2-functors, local adjunctions, homotopy theory, directed algebraic topology, fundamental 2-category 
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     author = {Marco Grandis},
     title = {Modelling fundamental 2-categories for directed homotopy},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n1.a2/}
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Marco Grandis. Modelling fundamental 2-categories for directed homotopy. Homology, homotopy, and applications, Tome 8 (2006) no. 1, pp. 31-70. doi : 10.4310/HHA.2006.v8.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n1.a2/

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