The powerset monad $\langle \mathrm{Pow}, \eta, \mu \rangle$ is understood on the category $\mathbf{Set}$ of sets and functions to do the following.
$$\mathrm{Pow} \colon \mathbf{Set} \rightarrow \mathbf{Set} $$
$\mathrm{Pow}$ sends a set to the set of subsets on that set.
This is all quite clear. Can we seat this monad on other categories? My first thought is any topos, but we can probably do better, i.e., seat it on a broader class of categories. What is the broad class and how do you define $\mathrm{Pow}$?