NationMaster - Encyclopedia: Monadic

In category theory, an adjunction is monadic or tripleable if it is equivalent to the adjunction given by the Eilenberg-Moore algebras of its associated monad. See monad (category theory).
In mathematical logic, a monadic logic is one that employs only unary relations.

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Categories: Disambiguation | Mathematical disambiguation Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... The existence of many pairs of adjoint functors is a major observation of the branch of mathematics known as category theory. ... In category theory, a monad or triple is a type of functor, together with two associated natural transformations. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, a monadic logic is one that employs only unary relations. ...

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Monad - definition of Monad in Encyclopedia (535 words)
	The monad begat the dyad, which begat the numbers, the numbers begat points, which begat lines, which begat two-dimensional entities, which begat three-dimensional entities, which begat bodies, which begat the four elements earth, water, fire and air, from which the rest of our world is built up.
	The Monad appears in the alchemical texts of the Hermetica, part four of the corpus is called The Cup or Monad.
	In pure functional programming languages such as Haskell, monads are used as data types that encapsulate the functional I/O-activity, in such a manner that the side-effects of IO are not allowed to spread out of the part of the program that is not functional (imperative).

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