Thosten Altenkirch ; James Chapman ; Tarmo Uustalu - Monads need not be endofunctors

lmcs:928 - Logical Methods in Computer Science, March 6, 2015, Volume 11, Issue 1 -
Monads need not be endofunctors

Authors: Thosten Altenkirch ; James Chapman ; Tarmo Uustalu

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 to a coreflection between relative monads and monads. Arrows are also an instance of relative monads.

Volume: Volume 11, Issue 1
Published on: March 6, 2015
Accepted on: June 25, 2015
Submitted on: May 4, 2011
Keywords: Computer Science - Programming Languages,Computer Science - Logic in Computer Science,Mathematics - Category Theory


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