  We develop the formal theory of monads, as established by Street, in
univalent foundations. This allows us to formally reason about various kinds of
monads on the right level of abstraction. In particular, we define the
bicategory of monads internal to a bicategory, and prove that it is univalent.
We also define Eilenberg-Moore objects, and we show that both Eilenberg-Moore
categories and Kleisli categories give rise to Eilenberg-Moore objects.
Finally, we relate monads and adjunctions in arbitrary bicategories. Our work
is formalized in Coq using the UniMath library.
