Rigidification of higher categorical structures

Caviglia, Giovanni¹ ; Horel, Geoffroy²

¹Institute for Mathematics, Astrophysics, and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands
²Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany

Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3533-3562

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.3533

Classification : 18C30, 18D35, 55U35, 18D05, 18D50
Keywords: internal operads, internal n-categories, limit sketches, model categories

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