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Complicial structures in the nerves of omega-categories

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Richard Steiner

It is known that strict omega-categories are equivalent through the
nerve functor to complicial sets and to sets with complicial
identities. It follows that complicial sets are equivalent to sets with
complicial identities. We discuss these equivalences. In particular we
give a conceptual proof that the nerves of omega-categories are
complicial sets, and a direct proof that complicial sets are sets with
complicial identities.

Keywords:
complicial set,complicial identities, omega-category

2010 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 24, pp 779-803.

Published 2013-09-01.

http://www.tac.mta.ca/tac/volumes/28/24/28-24.dvi

http://www.tac.mta.ca/tac/volumes/28/24/28-24.ps

http://www.tac.mta.ca/tac/volumes/28/24/28-24.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/24/28-24.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/24/28-24.ps

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