Algebraic Topology Seminar

Grothendieck Toposes are often considered as generalized spaces; indeed, every space gives rise to a topos of sheaves, and various invariants and constructions from (algebraic) topology can be generalized to the level of toposes. In this talk, I will introduce a newly discovered invariant called the isotropy group of a topos and illustrate by considering special cases such as continuous group actions and etale groupoids. On the one hand, this group plays a key role in the study of crossed toposes, a direct generalization of crossed modules. On the other hand, the isotropy group has connections to the theory of monoidal categories and certain aspects of lowdimensional topology. Based on joint work with Jonathon Funk.