Commutative diagram of function composition in a Kleisli category. Given a monad , consider a Kleisli category over that monad. Morphisms , , and in correspond to morphisms , , and in , respectively. The composition rule is . The Kleisli category shares the same objects as its underlying category. The morphisms of the Kleisli category (e.g.: and ) are embellished versions of the morphisms of its underlying category (e.g.: f and g), and they are derived from those of the underlying category by means of applying a monad to their codomains.