Categorical spectra and ℤ-categories

Abstract: Categorical spectra, developed by Stefanich, are a directed version of spectra where the suspension of pointed ∞-groupoids is replaced by that of pointed ω-categories. They are very useful for capturing stability phenomena in iterated categorifications, or for defining “∞-vector spaces”. In this talk, I will explain that they can be understood as a weak version of Lessard's ℤ-categories, a kind of category with arrows in all negative as well as positive dimensions, which allows for a more direct study of their structure.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)