Geodesic
Thin fillers in the cubical nerves of omega-categories
Theory and applications of categories, Tome 16 (2006), pp. 144-173

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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 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.

Classification : 18D05
Keywords: omega-category, cubical nerve, stratified precubical set, cubical T-complex, thin filler 
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     author = {Richard Steiner},
     title = {Thin fillers in the cubical nerves of omega-categories},
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     volume = {16},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a7/}
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Richard Steiner. Thin fillers in the cubical nerves of omega-categories. Theory and applications of categories, Tome 16 (2006), pp. 144-173. http://geodesic.mathdoc.fr/item/TAC_2006_16_a7/