Components of the Fundamental Category

Inthis article westudy the fundamental category (Goubault and Raussen, 2002 Goubault, 2002) of a partially ordered topological space (Nachbin, 1965 Johnstone, 1982), as arising in e.g. concurrency theory (Fajstrup et al., 1999). The \algebra" of dipaths modulo dihomotopy (the fundamental category) of such a pospace is essentially nite in a number of situations: We de ne a component category of a category of fractions with respect to a suitable system, which contains all relevant information. Furthermore, some of these simpler invariants are conjectured to also satisfy some form of a van Kampen theorem, as the fundamental category does (Goubault, 2002 Grandis, 2001). We end up by giving some hints about how to carry out some computations in simple cases.

• Type: Journal
• Year: 2004
• Where: ACS
• Authors: Lisbeth Fajstrup, Martin Raußen, Eric Goubault, Emmanuel Haucourt
• Keywords: ACS 2004, ACS 2007, Fundamental Category, Partially Ordered, Topological Space