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

Rune Haugseng

doi:10.1090/proc/13695

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

Algebraic Topology 2020-11-03 v2 Category Theory

Authors: 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.

Keywords

(∞,n)-categories Θ_n-spaces Segal spaces monad ∞-category n-globular spaces equivalence proof

Cite

@article{arxiv.1604.08480,
  title  = {On the equivalence between $\Theta_{n}$-spaces and iterated Segal spaces},
  author = {Rune Haugseng},
  journal= {arXiv preprint arXiv:1604.08480},
  year   = {2020}
}

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15 pages, v2: accepted version

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

Abstract

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