Omega-categories and chain complexes

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dc.creatorSteiner, Richard
dc.date2004-03-15
dc.date2004-05-17
dc.date.accessioned2026-07-07T05:06:24Z
dc.date.available2026-07-07T05:06:24Z
dc.descriptionThere 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.
dc.description18 pages; as published, with minor changes from version 1
dc.identifierhttps://arxiv.org/abs/math/0403237
dc.identifierhttp://arxiv.org/abs/math/0403237
dc.identifierHomology, Homotopy and Applications, vol 6(1), 2004, pp. 175-200
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70459
dc.subjectCategory Theory
dc.subject18D05
dc.titleOmega-categories and chain complexes
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