Monads as Extension Systems - No Iteration is Necessary

F. Marmolejo and R. J. Wood

We introduce a description of the algebras for a monad in terms of extension systems, similar to the one for monads given by Manes. We rewrite distributive laws for monads and wreaths in terms of this description, avoiding the iteration of the functors involved. We give a profunctorial explanation of why Manes' description of monads in terms of extension systems works.

Keywords: extension systems, monads, distributive laws, wreaths, profunctors

2000 MSC: 18C15, 18C20, 18D05

Theory and Applications of Categories, Vol. 24, 2010, No. 4, pp 84-113.

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