Dévissage for Algebraic K-theory of Small Stable ∞-categories

2026/01/21 by Chunhui Wei · 2 voices
Mathematics · #math.KT #math.CT

paper · pdf

arxiv published 2026/01/21 · arxiv updated 2026/05/18

Abstract

In this article, we extend the theorem of heart\citeBarwick₂015, which implies Quillen's dévissage theorem by \citeEfimov2025, to generic small stable ∞-categories. To be precise, we establish a necessary and sufficient condition under when an exact functor between stable ∞-categories induces isomorphisms of non-negative K-groups when this exact functor satisfies the dévissage condition.

Citations

• Theorem of the heart for Weibel's homotopy K-theory
• Some remarks on Quillen's Dévissage theorem
• Spherical adjunctions of stable ∞-categories and the relative S-construction
• Excision in algebraic K-theory revisited
• K-theoretic obstructions to bounded t-structures
• Higher traces, noncommutative motives, and the categorified Chern\n character
• Deriving Auslander's formula
• Derived category of filtered objects
• On the algebraic K-theory of higher categories
• A universal characterization of higher algebraic K-theory
• Higher Topos Theory
• Quasi-categories and Kan complexes
• Algebraic K-theory of spaces

Discussions

• Chunhui Wei D\'evissage for Algebraic K-theory of Small Stable $\infty$-categories https://arxiv.org/abs/2601.14626 [bsky, 0 points, 0 comments]
• Chunhui Wei: D\'evissage for Algebraic K-theory of Small Stable $\infty$-categories https://arxiv.org/abs/2601.14626 https://arxiv.org/pdf/2601.14626 https://arxiv.org/html/2601.14626 [bsky, 0 points, 0 comments]

Related

• A dévissage theorem of non-connective K-theory
• Weight structures and the algebraic K-theory of stable ∞-categories
• On exact categories and their stable envelopes
• Some remarks on Quillen's Dévissage theorem
• Every spectrum is the K-theory of a stable ∞-category