Geodesic
Omega-categories and chain complexes
Homology, homotopy, and applications, Tome 6 (2004) no. 1, pp. 175-200.

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

There are several ways to construct omega-categories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we call augmented directed complexes. This functor from augmented directed complexes to omega-categories has a left adjoint, and the adjunction restricts to an equivalence on a category of augmented directed complexes with good bases. The omega-categories equivalent to augmented directed complexes with good bases include the omega-categories associated to globes, simplexes and cubes; thus the morphisms between these omega-categories are determined by morphisms between chain complexes. It follows that the entire theory of omega-categories can be expressed in terms of chain complexes; in particular we describe the biclosed monoidal structure on omega-categories and calculate some internal homomorphism objects.
DOI : 10.4310/HHA.2004.v6.n1.a12
Classification : 18D05
Keywords: Omega-category, augmented directed complex 
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     author = {Richard Steiner},
     title = {Omega-categories and chain complexes},
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Richard Steiner. Omega-categories and chain complexes. Homology, homotopy, and applications, Tome 6 (2004) no. 1, pp. 175-200. doi : 10.4310/HHA.2004.v6.n1.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2004.v6.n1.a12/

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