On the equivalence between $\Theta_{n}$-spaces and iterated Segal spaces

Rune Haugseng

doi:10.1090/proc/13695

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arXiv · 1604.08480

On the equivalence between $\Theta_{n}$-spaces and iterated Segal spaces

Rune Haugseng

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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.

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Rune Haugseng. 2016-04-28. On the equivalence between $\Theta_{n}$-spaces and iterated Segal spaces. https://doi.org/10.1090/proc/13695

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