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- W2997474705 abstract "We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-performing machines. Monad-comonad interaction laws are monoid objects of the monoidal category of functor-functor interaction laws. We show that, for suitable generalizations of the concepts of dual and Sweedler dual, the greatest functor resp. monad interacting with a given functor or comonad is its dual while the greatest comonad interacting with a given monad is its Sweedler dual. We relate monad-comonad interaction laws to stateful runners. We show that functor-functor interaction laws are Chu spaces over the category of endofunctors taken with the Day convolution monoidal structure. Hasegawa's glueing endows the category of these Chu spaces with a monoidal structure whose monoid objects are monad-comonad interaction laws." @default.
- W2997474705 created "2020-01-10" @default.
- W2997474705 creator A5041431787 @default.
- W2997474705 creator A5053982125 @default.
- W2997474705 creator A5074922343 @default.
- W2997474705 date "2019-12-31" @default.
- W2997474705 modified "2023-09-23" @default.
- W2997474705 title "Interaction laws of monads and comonads" @default.
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- W2997474705 doi "https://doi.org/10.48550/arxiv.1912.13477" @default.
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