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Theoretical Computer Science
Volume 280, Issues 1-2, 30 May 2002, Pages 137-162
 
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doi:10.1016/S0304-3975(01)00024-X    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2002 Elsevier Science B.V. All rights reserved.

Combining a monad and a comonad

John Power1, Corresponding Author Contact Information, E-mail The Corresponding Author, , a and Hiroshi Watanabe2, E-mail The Corresponding Author, , b

a Laboratory for the Foundations of Computer Science, Division of Informatics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK b Semantics Group, Osaka LERC, Electrotechnical Laboratory, Amagasaki 661-0974, Japan

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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