Affiliation: | 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 |
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. |