Algebra/Topology seminar

Speaker: Mark Penney (MPIM Bonn)

Title: Simplicial spaces, lax algebras and the 2-Segal condition

Abstract: Simplicial objects satisfying the Segal conditions are used throughout homotopy theory and higher category theory to encode coherently associative algebras. Recently, Dyckerhoff–Kapranov and Galvez-Carrillo–Kock–Tonks independently introduced a generalisation of Rezk’s Segal conditions, the 2-Segal conditions. They showed that simplicial objects satisfying the 2-Segal conditions encode algebra objects in ∞-categories of spans. 

After providing a general introduction to 2-Segal spaces, including the examples coming from Waldhausen's S-construction, I will explain the exact role played by the 2-Segal condition in the construction of these algebras.