Multiplicative structures on algebraic $K$-theory

Abstract

The algebraic $K$-theory of Waldhausen $\infty$-categories is the functor corepresented by the unit object for a natural symmetric monoidal structure. We therefore regard it as the stable homotopy theory of homotopy theories. In particular, it respects all algebraic structures, and as a result, we obtain the Deligne Conjecture for this form of $K$-theory.