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

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arxiv 2304.05965 v1 pith:MZVXWRSP submitted 2023-04-12 math.CT math.AT

Timothy Campion , Yuki Maehara This is my paper · ORCID
classification math.CTmath.AT
keywords graycategoriesinftytensorproductcategorymodel-independentagrees
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On The Telescopic Picard Group

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    For all primes p and heights n, Pic(Sp_{T(n)}) contains Z_p × Z/(a_p(p^n−1)), lifting the known K(n)-local subgroup.

  2. Higher Semiadditive Character Theory

    math.AT 2026-07 accept novelty 7.0 of 10

    Every ∞-commutative monoid has a universal (n−t)-fold semiadditive character that blue-shifts height, recovers the transchromatic character on Morava E-theory, and computes L_Q(S^A_{K(n)}) via GL_{n−t}(Z_p)-fixed points.

  3. The Gray Product of $(\infty, n)$-Categories via Lax Grids

    math.CT 2026-06 unverdicted novelty 7.0 of 10

    Univalent Segal sheaves on lax grids are monoidally equivalent to (∞,n)-categories with Campion's Gray product, constructed by Day convolution.

  4. On the squares functor and the Gaitsgory-Rozenblyum conjectures

    math.CT 2025-07 conditional novelty 7.0 of 10

    The authors prove that Gr(Ch×Dv) is naturally equivalent to C⊗D, settling Gaitsgory and Rozenblyum's final conjecture, and establish a companion-based universal property of the squares functor.

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