On the equivalence between Θ_{𝑛}-spaces and iterated Segal spaces

Haugseng, Rune

doi:10.1090/proc/13695

On the equivalence between $\Theta _{n}$-spaces and iterated Segal spaces
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Proc. Amer. Math. Soc. 146 (2018), 1401-1415

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 $\mathbf {\Theta }_{n}$-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.

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