A comparison of Segal and Waldhausen K-theory

Higher algebraic K-theory is a powerful invariant which was originally defined for rings, but has since grown far beyond its initial scope to encompass increasingly rich and intricate settings. There are many different constructions of algebraic K-theory, reflecting the range of uses and perspectives encompassed by the theory. In this talk, I will describe a comparison between Waldhausen’s K-theory construction and Segal’s K-theory of symmetric monoidal categories. Precisely, given a symmetric monoidal category, we construct a Waldhausen category with an equivalent K-theory spectrum.