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arXiv · 1511.01119

Rigidification of higher categorical structures

Giovanni Caviglia·Geoffroy Horel
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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 $Θ_n$-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. 2016-05-16. Rigidification of higher categorical structures. https://doi.org/10.2140/agt.2016.16.3533

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