Fixpoint toposes

Richard Garner – 26 June 2019

Last week I mentioned a theorem: the category of fixpoints of an accessible pullback-preserving endofunctor of a Grothendieck topos is a Grothendieck topos. This week I'll prove this theorem. This builds on results by Pare, Rosebrugh and Wood, and by Johnstone, Power, Tsujishita, Watanabe and Worrell. I'll also discuss what happens when you remove the qualifier "Grothendieck".