Dévissage in Waldhausen K-theory

The aim of this project is to generalize Quillen’s dévissage theorem in algebraic K-theory:

Theorem. Let $C$ be an exact subcategory of an abelian category $D$, closed under subobjects and quotients. If every object of $D$ has a finite filtration with filtration quotients in $C$, then $KC \simeq KD$.

The goal of the proposed project is to prove a generalized dévissage theorem in Waldhausen K-theory with methods that have not been previously applied to this question.

This project, which is joint with Wojciech Chachólski, received funding from the Knut and Alice Wallenberg foundation to hire a postdoc for two years from 2017; the application contains more information about the project and our group.