Geodesic
Models and van Kampen theorems for directed homotopy theory
Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 185-202.

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

We study topological spaces with a distinguished set of paths, called directed paths. Since these directed paths are generally not reversible, the directed homotopy classes of directed paths do not assemble into a groupoid, and there is no direct analog of the fundamental group. However, they do assemble into a category, called the fundamental category. We define models of the fundamental category, such as the fundamental bipartite graph, and minimal extremal models which are shown to generalize the fundamental group. In addition, we prove van Kampen theorems for subcategories, retracts, and models of the fundamental category.
DOI : 10.4310/HHA.2009.v11.n1.a9
Classification : 55Pxx, 68Q85, 18A30, 18A40, 55Uxx
Keywords: directed homotopy, fundamental category, van Kampen theorem, $d$-space, reflective subcategory, coreflective subcategory, past retract, future retract, extremal model, fundamental bipartite graph 
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     author = {Peter Bubenik},
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Peter Bubenik. Models and van Kampen theorems for directed homotopy theory. Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 185-202. doi : 10.4310/HHA.2009.v11.n1.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a9/

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