On the squares functor and the Gaitsgory-Rozenblyum conjectures

2025/07/10 by Félix Loubaton, Jaco Ruit, Loubaton, Félix +1 · 1 citation
Mathematics · #18N10 #18N65 #55U35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.07807

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Homotopy coherent companionships and conjunctions
• Equivalence of cubical and simplicial approaches to (∞,n)-categories
• Gray tensor product and saturated N-complicial sets
• A cubical model for (∞, n)-categories
• Higher Topos Theory

Cited by

• Zigzags and free adjunctions

Related

• (∞,n)-categories in context
• Comparing lax functors of (∞,2)-categories
• Algebraic K-theory for squares categories
• A short course on ∞-categories
• On the equivalence of all models for (∞,2)-categories