On the equivalence between ${\Theta }_n$-spaces and iterated Segal spaces

Abstract

We give a new proof of the equivalence between two of the main models for $(\infty ,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the ${\Theta }_n$-spaces of Rezk, by proving that these are algebras for the same monad on the $\infty$-category of $n$-globular spaces. The proof works for a broad class of $\infty$-categories that includes all $\infty$-topoi.

15 pages, v2: accepted version

Cited by in corpus (4)

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• Envelopes for Algebraic Patterns
• Segalification and the Boardman-Vogt tensor product
• Discreteness and completeness for ${\Theta }_n$-models of $(\infty ,n)$-categories