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2009 Models and van Kampen theorems for directed homotopy theory
Peter Bubenik
Homology Homotopy Appl. 11(1): 185-202 (2009).


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.


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Peter Bubenik. "Models and van Kampen theorems for directed homotopy theory." Homology Homotopy Appl. 11 (1) 185 - 202, 2009.


Published: 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1163.55007
MathSciNet: MR2506132

Primary: 55P99 , 68Q85
Secondary: 18A30 , 18A40 , 55U99

Keywords: $D$-space , coreflective subcategory , Directed homotopy , extremal model , fundamental bipartite graph , fundamental category , future retract , past retract , reflective subcategory , van Kampen theorem

Rights: Copyright © 2009 International Press of Boston

Vol.11 • No. 1 • 2009
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