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arXiv · 2304.05965

A model-independent Gray tensor product for $(\infty,2)$-categories

Timothy Campion·Yuki Maehara
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Abstract

We construct a (lax) Gray tensor product of $(\infty,2)$-categories and characterize it via a model-independent universal property. Namely, it is the unique monoidal biclosed structure on the $\infty$-category of $(\infty,2)$-categories which agrees with the classical Gray tensor product of strict 2-categories when restricted to the Gray cubes (i.e. the Gray tensor powers $[1]^{\otimes n}$ of the arrow category).

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Timothy Campion, Yuki Maehara. 2023-04-12. A model-independent Gray tensor product for $(\infty,2)$-categories. https://arxiv.org/abs/2304.05965

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