D\'evissage for Algebraic K-theory of Small Stable $\infty$-categories

TL;DR

This paper generalizes the de9vissage theorem for algebraic K-theory to small stable d8-infinity categories, providing conditions under which exact functors induce isomorphisms of K-groups.

Contribution

It extends the heart theorem to a broader class of small stable d8-infinity categories, establishing necessary and sufficient conditions for K-group isomorphisms.

Findings

Established a necessary and sufficient condition for exact functors to induce K-group isomorphisms.

Extended the heart theorem to generic small stable d8-infinity categories.

Provided a criterion for when de9vissage applies in this setting.

Abstract

In this article, we extend the theorem of heart\cite{Barwick_2015}, which implies Quillen's d\'evissage theorem by \cite{Efimov2025}, to generic small stable $\infty$-categories. To be precise, we establish a necessary and sufficient condition under when an exact functor between stable $\infty$-categories induces isomorphisms of non-negative $K$-groups when this exact functor satisfies the d\'evissage condition.