  We introduce and study functor-functor and monad-comonad interaction laws as
mathematical objects to describe interaction of effectful computations with
behaviors of effect-performing machines. Monad-comonad interaction laws are
monoid objects of the monoidal category of functor-functor interaction laws. We
show that, for suitable generalizations of the concepts of dual and Sweedler
dual, the greatest functor resp. monad interacting with a given functor or
comonad is its dual while the greatest comonad interacting with a given monad
is its Sweedler dual. We relate monad-comonad interaction laws to stateful
runners. We show that functor-functor interaction laws are Chu spaces over the
category of endofunctors taken with the Day convolution monoidal structure.
Hasegawa's glueing endows the category of these Chu spaces with a monoidal
structure whose monoid objects are monad-comonad interaction laws.
