Australian Category Seminar

The isotropy group of a category $\mathcal{C}$ is a group object in $\mathcal{C}$ which is universal among groups which act on every object of $\mathcal{C}$ and act on themselves by conjugation. The notation was introduced by Funk, Hofstra, and Steinberg, though it is closely related to Freyd’s notion of the core of a topos. This talk will give an overview of some aspects of the theory of isotropy.