Algebra/Topology seminar
Speaker: Jonte Gödicke
Title: Which 2-Segal objects are rigid?
Abstract: In the study of Topological Field Theories in dimension 3 rigid tensor categories are of fundamental importance. Well-known examples of those arise from finite groups via a linearization construction. More generally this construction can be applied to build tensor categories from 2-Segal spaces, also known as decomposition spaces.
In this talk, I will answer the question posed in the title and classify those 2-Segal spaces that induce rigid tensor categories via linearization. For this, I will utilize a 2-categorical formulation of rigidity to translate questions about the rigidity of these monoidal structures to questions about higher algebra in span categories.