Abstract
Just as every topos contains a canonical locale, its subobject
classifier, every Grothendieck topos contains a canonical group, its
isotropy group. In this talk, I will first explain the nature of this group,
and develop some of the basic theory of isotropy quotients of toposes. After
that, I will explain how isotropy groups give rise to interesting (balanced,
closed) monoidal structures on certain toposes, generalizing ideas
from Freyd-Yetter.