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On the squares functor and the Gaitsgory-Rozenblyum conjectures

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arxiv 2507.07807 v2 pith:53ULBHYG submitted 2025-07-10 math.CT math.AT

On the squares functor and the Gaitsgory-Rozenblyum conjectures

classification math.CT math.AT
keywords conjecturesfunctorgaitsgory-rozenblyuminftysquaresaimsalgebraicalong
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In the seminal work of Gaitsgory and Rozenblyum on derived algebraic geometry, eight conjectures regarding the theory of $(\infty,2)$-categories are stated. This paper aims to clarify the status of these claims, and to provide a proof for the last remaining open one. Along the way, we demonstrate the universal property of the so-called squares functor, a construction that plays an important role in the $(\infty,2)$-categorical foundations of Gaitsgory-Rozenblyum.

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Cited by 3 Pith papers

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

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    Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.

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

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    New model of (∞,n)-categories as Segal sheaves on lax grids yields direct Day convolution construction of Gray tensor product agreeing with Campion's.

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

    math.CT 2026-06 accept novelty 7.0

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