Group-completion K-theory via Waldhausen categories

There are various constructions of higher algebraic K-theory that are applicable to different kinds of categorical inputs, and these constructions agree in many settings — most notably, for the algebraic K-theory of a ring. In this talk we will discuss a new, general comparison between Waldhausen’s S-dot construction and Segal’s group completion K-theory for symmetric monoidal categories: given any symmetric monoidal category, we construct a Waldhausen category with an equivalent K-theory spectrum. As a consequence, we show that every connective spectrum is equivalent to the K-theory of some ordinary Waldhausen category. This talk is based on joint work with David Chan.