Non-additive functors and Euler characteristics

TL;DR

This paper explores how certain functors between abelian categories induce maps on Grothendieck groups, extending classical results by relating to derived functors and generalizing Dold's theorem.

Contribution

It introduces a framework for non-additive functors to induce maps on Grothendieck groups under finiteness conditions, broadening the scope of classical theorems.

Findings

Established conditions for functors to induce Grothendieck group maps

Connected the construction to derived functors of Dold and Puppe

Generalized a theorem of Dold to non-additive contexts

Abstract

We show under suitable finiteness conditions that a functor between abelian categories induces a (not necessarily additive) map between their Grothendieck groups. This is related to the derived functors of Dold and Puppe, and generalizes a theorem of Dold.