Equivariant Pitts Monads

**Abstract:** In the first part of this talk, which is a sequel to
my previous talk "Pitts Monads and a Lax Descent Theorem", I will
begin by completing my exposition of the latter as follows. I will
sketch the proof of the lax descent theorem and then
briefly review the applications obtained. In the second part of this
talk, I will introduce a notion of an 'equivariant
Pitts monad' on a 2-category **K** (with bipullbacks and a pseudoterminal
object *T*). Although not necessary for the general
lax descent theorem, as we have shown, this stronger notion permits a
certain passage from effective lax descent to
effective descent. This passage will be illustrated in the case of the
lower and upper powerlocale monads.