Omega-categories and chain complexes. (English) Zbl 1071.18005

The preceding constructions of \(\omega\)-categories from combinatorial structures are not really functorial. One has here a construction as a functor on a category of chain complexes with additional structure called augmented directed complexes. This functor has a left adjoint and the adjunction restricts to equivalence between certain full subcategories: free chain complexes with good bases and \(\omega\)-categories having good sets of generators.
In this way, the entire theory of \(\omega\)-categories can be expressed in terms of chain complexes (biclosed monoidal structure on \(\omega\)-categories, calculation of some internal morphisms objects,…).


18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18G35 Chain complexes (category-theoretic aspects), dg categories
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