On the universal property of Waldhausen's K-theory

TL;DR

This paper proves that Waldhausen's K-theory functor has a universal property as the additive target of the global Euler characteristic, and extends this property to a broad class of functors.

Contribution

It establishes the universal property of Waldhausen's K-theory and demonstrates that many functors admit an additivization.

Findings

Waldhausen's K-theory is the universal additive functor from Waldhausen categories.

The global Euler characteristic is characterized as the universal additive invariant.

Many functors can be extended to their additivizations within this framework.

Abstract

In this note we show that Waldhausen's K-theory functor from Waldhausen categories to spaces has a universal property: It is the target of the "universal global Euler characteristic", in other words, the "additivization" of the functor sending a Waldhausen category C to obj(C) . We also show that a large class of functors possesses such an additivization.