Continuous K-theory and polynomial functors

Waldhausen K-theory can be defined as an invariant of small stable $\infty$-categories, and is characterized (following work of Blumberg-Gepner-Tabuada and Barwick) by the property that it converts Verdier quotient sequences of stable $\infty$-categories to fiber sequences. Recently, Efimov defined the continuous K-theory of the larger class of dualizable presentable stable $\infty$-categories, which is important for applications to the K-theory of analytic spaces.

In work with Barwick, Glasman, and Nikolaus, we showed that polynomial functors induce natural (non-additive) maps in Waldhausen K-theory. In this lecture, I'll give an overview of some of these constructions and explain how the polynomial functoriality extends to Efimov K-theory.