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2004 Omega-categories and chain complexes
Richard Steiner
Homology Homotopy Appl. 6(1): 175-200 (2004).


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.


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Richard Steiner. "Omega-categories and chain complexes." Homology Homotopy Appl. 6 (1) 175 - 200, 2004.


Published: 2004
First available in Project Euclid: 13 February 2006

zbMATH: 1071.18005
MathSciNet: MR2061574

Primary: 18D05

Rights: Copyright © 2004 International Press of Boston


Vol.6 • No. 1 • 2004
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