Copyright © 2002 Elsevier Science B.V. All rights reserved.
Combining a monad and a comonad
Available online 17 May 2002.
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Abstract
We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg–Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis.
Author Keywords: 2-Category; Monad; Comonad; Algebra; Coalgebra; Kleisli construction; Distributive law; Bialgebra







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