The powerset monad on quantale-valued sets

For a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric $\mathcal{Q}$-categories. In particular, the (covariant) powerset monad on the category of quantale-valued sets is precisely formulated.