## A model-independent construction of the Gray monoidal structure for (∞,2)-categories

### Alexander Campbell – 14 October 2020

In this talk I will describe joint work with Dr Yuki Maehara in which we give a model-independent (i.e. a purely ∞-categorical) construction of the (non-symmetric) Gray monoidal structure on the ∞-category of (∞,2)-categories. Our construction is a generalisation to the ∞-categorical setting of a construction of the Gray monoidal structure for 2-categories due to Ross Street, which uses the techniques from Brian Day's PhD thesis for extending a monoidal structure along a dense functor. The proof of our construction uses, among other things, the results from Yuki's recent PhD thesis on the Gray tensor product for 2-quasi-categories. I will also mention a few of the open problems concerning the Gray monoidal structure for (∞,2)-categories, and explain how our results can be used to simplify (though not yet solve) one of these problems.

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