  The original purpose of component-based development was to provide techniques
to master complex software, through composition, reuse and parametrisation.
However, such systems are rapidly moving towards a level in which software
becomes prevalently intertwined with (continuous) physical processes. A
possible way to accommodate the latter in component calculi relies on a
suitable encoding of continuous behaviour as (yet another) computational
effect. This paper introduces such an encoding through a monad which, in the
compositional development of hybrid systems, may play a role similar to the one
played by the 1+, powerset, and distribution monads in the characterisation of
partial, non deterministic and probabilistic components, respectively. This
monad and its Kleisli category provide a setting in which the effects of
continuity over (different forms of) composition can be suitably studied.
