Dualizable presentable ∞-categories

2024/10/28 by Maxime Ramzi, Ramzi, Maxime · 1 citation
Medicine · Mathematics · #Intracranial Aneurysms: Treatment and Complications #Homotopy and Cohomology in Algebraic Topology #Vascular Malformations Diagnosis and Treatment

paper · pdf · doi:10.48550/arxiv.2410.21537

Abstract

We prove that for any presentably symmetric monoidal ∞-category V, the ∞-category Mod_V(Pr^L)^dbl of dualizable presentable V-modules and internal left adjoints between them is itself presentable. Along the way, we survey formal properties of these dualizable \mathcal V-modules. We pay close attention to the case of the ∞-category of spectra, where we survey the foundational properties of ``compact morphisms''.

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