UCalgary Peripatetic Seminar: Tanner Carawan

Waldhausen’s S_\bullet-construction gives a way to define the algebraic K-theory space of a category with cofibrations. Specifically, the K-theory space of a category with cofibrations C can be defined as the loop space of the realization of the simplicial topological space |iS_\bullet C |. Dyckerhoff and Kapranov observed that if C is chosen to be a proto-exact category, then this simplicial topological space is 2-Segal. A natural question is then what variants of this S_\bullet-construction give 2-Segal spaces. In this talk, we give the necessary background in this area and discuss work in progress that aims to address the preceding question.