Geodesic
Equivalence of Categories of Precubical Sets and Transitional Chu-Spaces, Preserving the Property of Morphisms to be Open
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 123-145

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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.
Keywords: precubical sets, Chu-space, $di$-topology, equivalence of category.
Mots-clés : open morphism, $di$-homotopy 
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     author = {E. S. Oshevskaya},
     title = {Equivalence of {Categories} of {Precubical} {Sets} and {Transitional} {Chu-Spaces,} {Preserving} the {Property} of {Morphisms} to be {Open}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {123--145},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a8/}
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E. S. Oshevskaya. Equivalence of Categories of Precubical Sets and Transitional Chu-Spaces, Preserving the Property of Morphisms to be Open. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 123-145. http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a8/