Title: All K-theory is squares K-theory: constructing a derived Euler characteristic
Abstract: Combinatorial (or “cut-and-paste”) K-theory is a modern approach to the study of classical scissors congruence groups, inspired by algebraic K-theory of Waldhausen categories, and can be applied to other geometric settings as well, such as the categories of varieties and semi-algebraic sets. We present the K-theory of squares category as a framework that unifies Waldhausen K-theory as well as many instances of combinatorial K-theory. As an application, we lift the Euler characteristic for definable sets in an o-minimal structure to a map of K-theory spectra.