Gray tensor products and Lax functors of (∞,2)-categories

0545388 - MÚ 2022 RIV US eng J - Journal Article
Gagna, A. - Harpaz, Y. - Lanari, Edoardo
Gray tensor products and Lax functors of (∞,2)-categories.
Advances in Mathematics. Roč. 391, November (2021), č. článku 107986. ISSN 0001-8708. E-ISSN 1090-2082
Grant - others:AV ČR(CZ) AP1801
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : Gray tensor product * higher category theory * homotopy theory
OECD category: Pure mathematics
Impact factor: 1.675, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.aim.2021.107986

We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is associative and forms a left Quillen bifunctor with respect to the bicategorical model category of Lurie. We then introduce a notion of oplax functor in this setting, and use it in order to characterize the Gray tensor product by means of a universal property. A similar characterization was used by Gaitsgory and Rozenblyum in their definition of the Gray product, thus giving a promising lead for comparing the two settings.
Permanent Link: http://hdl.handle.net/11104/0322087