Equivalence of Categories of Precubical Sets and Transitional Chu-Spaces, Preserving the Property of Morphisms to be Open

E. S. Oshevskaya

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 123-145

Résumé

The intention of the paper is to show the applicability of the directed algebraic topology to establish the close categorical relationships between geometrical models of concurrency — precubical sets and transitional Chu-spaces. In particular, we start with introducing categories of the models under consideration. Then, we construct and study the universal di-covering functor from the category of precubical sets to the category of simply di-connected counterpart of precubical sets. Finally, an equivalence of the categories of transitional Chu-spaces and simply di-connected precubical sets is established, preserving an important property of morphisms to be open.

Détail

Keywords: precubical sets, Chu-space, $di$-topology, equivalence of category.
Mots-clés : open morphism, $di$-homotopy

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