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

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arxiv 2311.00205 v1 pith:ETQGXMXO submitted 2023-11-01 math.CT math.AT

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

classification math.CT math.AT
keywords categoriesinftygrayproducttensormodelsauthorcarry
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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