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2016 Rigidification of higher categorical structures
Giovanni Caviglia, Geoffroy Horel
Algebr. Geom. Topol. 16(6): 3533-3562 (2016). DOI: 10.2140/agt.2016.16.3533

Abstract

Given a limit sketch in which the cones have a finite connected base, we show that a model structure of “up to homotopy” models for this limit sketch in a suitable model category can be transferred to a Quillen-equivalent model structure on the category of strict models. As a corollary of our general result, we obtain a rigidification theorem which asserts in particular that any Θn–space in the sense of Rezk is levelwise equivalent to one that satisfies the Segal conditions on the nose. There are similar results for dendroidal spaces and n–fold Segal spaces.

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Giovanni Caviglia. Geoffroy Horel. "Rigidification of higher categorical structures." Algebr. Geom. Topol. 16 (6) 3533 - 3562, 2016. https://doi.org/10.2140/agt.2016.16.3533

Information

Received: 13 November 2015; Revised: 16 May 2016; Accepted: 16 May 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1354.18004
MathSciNet: MR3584266
Digital Object Identifier: 10.2140/agt.2016.16.3533

Subjects:
Primary: 18C30, 18D35, 55U35
Secondary: 18D05, 18D50

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 6 • 2016
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