The Gray tensor product of $(\infty ,n)$-categories

Abstract

In this note, we leverage the author's pasting theorem for $(\infty ,n)$-categories to construct new models of $(\infty ,n)$-categories for all $n\le \infty$, as presheaves on certain categories of computads. Among these new models are some which facilitate a construction of the Gray tensor product of $(\infty ,n)$-categories Day convolution and reflection, which we carry out here. After constructing this Gray tensor product of $(\infty ,n)$-categories, we characterize it via several model-independent universal properties.

20 pages, comments welcome!