Locally rigid ∞-categories

2024/10/28 by Maxime Ramzi, Ramzi, Maxime
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2410.21524

openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the theory of locally rigid and rigid symmetric monoidal ∞-categories over an arbitrary base V\inCAlg(Pr^L). Among other things, we prove that every locally rigid commutative V-algebra arises as a ``completion'' of a rigid commutative V-algebra. Along the way, we introduce and study ``V-atomic morphisms'', which are analogues of compact morphisms over an arbitrary base V.

Related

• Rigid Algebras and Cospans
• Formal category theory in ∞-equipments II: Lax functors, monoidality and fibrations
• Invertible exterior powers
• ∞-operads as symmetric monoidal ∞-categories
• Monoidal Relative Categories Model Monoidal ∞-Categories