English

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

Algebraic Topology 2020-07-01 v1 Category Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2006.14495,
  title  = {Gray tensor products and lax functors of $(\infty,2)$-categories},
  author = {Andrea Gagna and Yonatan Harpaz and Edoardo Lanari},
  journal= {arXiv preprint arXiv:2006.14495},
  year   = {2020}
}