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

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. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study provides a definition and properties of the Gray tensor product in the setting of scaled simplicial sets, introduces the concept of oplax functor, and characterizes the Gray tensor product through a universal property. The results of this study offer a promising direction for comparing two concepts in different settings.