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arXiv · 2507.07807

On the squares functor and the Gaitsgory-Rozenblyum conjectures

Félix Loubaton·Jaco Ruit
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Abstract

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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Félix Loubaton, Jaco Ruit. 2025-07-10. On the squares functor and the Gaitsgory-Rozenblyum conjectures. https://arxiv.org/abs/2507.07807

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