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


Author: Rune Haugseng
Journal: Proc. Amer. Math. Soc. 146 (2018), 1401-1415
MSC (2010): Primary 18D05, 55U40
DOI: https://doi.org/10.1090/proc/13695
Published electronically: December 26, 2017
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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 $ \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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Additional Information

Rune Haugseng
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
Email: haugseng@math.ku.dk

DOI: https://doi.org/10.1090/proc/13695
Received by editor(s): April 28, 2016
Received by editor(s) in revised form: January 29, 2017
Published electronically: December 26, 2017
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2017 Rune Haugseng

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