Localisation theorems for the connective K-theory of exact categories

2025/10/08 by Christoph Winges, Winges, Christoph
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.2510.07170

openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We prove a localisation theorem for the K-theory of filtering subcategories of exact ∞-categories which subsumes the localisation theorem for stable ∞-categories, Quillen's localisation theorem for abelian categories, and Schlichting's localisation theorem for s-filtering subcategories.

Citations

• The presentable stable envelope of an exact category
• Some remarks on Quillen's Dévissage theorem
• On exact categories and their stable envelopes
• A short proof that Rezk's nerve is fully faithful
• A short proof of the straightening theorem
• Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity
• Controlled objects in left-exact ∞-categories and the Novikov conjecture
• Topological cyclic homology
• A spectrum-level Hodge filtration on topological Hochschild homology

Related

• The localisation theorem for the K-theory of stable ∞-categories
• Localization of extriangulated categories
• K-theory and localizing invariants of large categories
• Dwyer-Kan localization revisited
• Devissage and Localization for the Grothendieck Spectrum of Varieties