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Monads need not be endofunctors

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&nbsp;[&hellip;]

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When is a container a comonad?

Danel Ahman ; James Chapman ; Tarmo Uustalu.

Abbott, Altenkirch, Ghani and others have taught us that many parameterized datatypes (set functors) can be usefully analyzed via container representations in terms of a set of shapes and a set of positions in each shape. This paper builds on the observation that datatypes often carry additional&nbsp;[&hellip;]

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