Complicial structures in the nerves of omega-categories
Richard Steiner
TL;DR
This paper explores the relationships between strict omega-categories, complicial sets, and sets with complicial identities, providing conceptual and direct proofs of their equivalences.
Contribution
It offers a conceptual proof that the nerves of omega-categories are complicial sets and a direct proof that complicial sets are sets with complicial identities.
Findings
Nerves of omega-categories are complicial sets
Complicial sets are equivalent to sets with complicial identities
Provides conceptual and direct proofs of these equivalences
Abstract
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra