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

Timothy Campion

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arXiv · 2311.00205

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

Timothy Campion

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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 $n \leq \infty$, 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.

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Timothy Campion. 2023-11-01. The Gray tensor product of $(\infty,n)$-categories. https://arxiv.org/abs/2311.00205

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