Seminar

The structure of a 2-Segal space encodes data like that of a category, but for which composition need not always exist or be unique, yet is still associative.  It was shown by Dyckerhoff and Kapranov, and independently by G\'alvez-Carrillo, Kock, and Tonks, that applying Waldhausen's S-construction to an exact category results in a 2-Segal space.  In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we expand the input of this construction in such a way that the S-construction defines an equivalence of homotopy theories, as well as recovers other known generalizations.  In work in progress with Zakharevich, we show that this general input has a close relationship with the CGW categories of Campbell and Zakharevich, which are also designed to be a very general context in which algebraic K-theory constructions can be made.