On the squares functor and the Gaitsgory-Rozenblyum conjectures
Abstract
In the seminal work of Gaitsgory and Rozenblyum on derived algebraic geometry, eight conjectures regarding the theory of (∞,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 (∞,2)-categorical foundations of Gaitsgory-Rozenblyum.
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