Monads need not be endofunctors

Thosten Altenkirch, James Chapman, Tarmo Uustalu, Luke Ong
2015 Logical Methods in Computer Science  
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise
more » ... monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads.
doi:10.2168/lmcs-11(1:3)2015 fatcat:appnosjlevbovhd2yf2trs6tgm