Mathematics – Category Theory
Scientific paper
2006-01-16
Theory and Applications of Categories 16 (2006), No. 8, 144-173
Mathematics
Category Theory
Revised version to appear in Theory and Applications of Categories; changed terminology; additional figures, examples and refe
Scientific paper
It is shown that the cubical nerve of a strict omega-category is a sequence of sets with cubical face operations and distinguished subclasses of thin elements satisfying certain thin filler conditions. It is also shown that a sequence of this type is the cubical nerve of a strict omega-category unique up to isomorphism; the cubical nerve functor is therefore an equivalence of categories. The sequences of sets involved are in effect the analogues of cubical T-complexes appropriate for strict omega-categories. Degeneracies are not required in the definition of these sequences, but can in fact be constructed as thin fillers. The proof of the thin filler conditions uses chain complexes and chain homotopies.
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