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Article Dans Une Revue Advances in Mathematics Année : 2021

Gray tensor products and lax functors of $(\infty,2)$-categories

Résumé

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.

Dates et versions

hal-02926635 , version 1 (31-08-2020)

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Andrea Gagna, Yonatan Harpaz, Edoardo Lanari. Gray tensor products and lax functors of $(\infty,2)$-categories. Advances in Mathematics, 2021, 391, ⟨10.1016/j.aim.2021.107986⟩. ⟨hal-02926635⟩
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