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Thin fillers in the cubical nerves of omega-categories

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Richard Steiner

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.

Keywords:
omega-category, cubical nerve, stratified precubical
set, cubical T-complex, thin filler

2000 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 16, 2006,
No. 8, pp 144-173.

http://www.tac.mta.ca/tac/volumes/16/8/16-08.dvi

http://www.tac.mta.ca/tac/volumes/16/8/16-08.ps

http://www.tac.mta.ca/tac/volumes/16/8/16-08.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/8/16-08.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/8/16-08.ps

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