Look up monad in Wiktionary, the free dictionary.
Monad may refer to:
Monad may refer to:
Radical may refer to:
Universal algebra is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study.
Abelian may refer to:
Factor, a Latin word meaning "who/which acts", may refer to:
Term may refer to:
Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole.
Top most commonly refers to:
In category theory, a branch of mathematics, a monad is a triple consisting of a functor T from a category to itself and two natural transformations that satisfy the conditions like associativity. For example, if are functors adjoint to each other, then together with determined by the adjoint relation is a monad.
Equivalence or Equivalent may refer to:
In functional programming, a monad is a structure that combines program fragments (functions) and wraps their return values in a type with additional computation. In addition to defining a wrapping monadic type, monads define two operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type. General-purpose languages use monads to reduce boilerplate code needed for common operations. Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effects.
Monadic may refer to:
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of identities. For example, the groups form a variety of algebras, as do the abelian groups, the rings, the monoids etc. According to Birkhoff's theorem, a class of algebraic structures of the same signature is a variety if and only if it is closed under the taking of homomorphic images, subalgebras, and (direct) products. In the context of category theory, a variety of algebras, together with its homomorphisms, forms a category; these are usually called finitary algebraic categories.
In some Gnostic systems, the supreme being is known as the Monad, the One, the Absolute, Aiōn Teleos, Bythos, Proarchē, Hē Archē, the Ineffable Parent, and/or the primal Father. The Monad is an adaptation of concepts of the monad in Greek philosophy to Christian belief systems.
SO or so may refer to:
In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock Beck in about 1964. It is often stated in dual form for comonads. It is sometimes called the Beck tripleability theorem because of the older term triple for a monad.
In computer science, arrows or bolts are a type class used in programming to describe computations in a pure and declarative fashion. First proposed by computer scientist John Hughes as a generalization of monads, arrows provide a referentially transparent way of expressing relationships between logical steps in a computation. Unlike monads, arrows don't limit steps to having one and only one input. As a result, they have found use in functional reactive programming, point-free programming, and parsers among other applications.
K, or k, is the eleventh letter of the English alphabet.
The term monad is used in some cosmic philosophy and cosmogony to refer to a most basic or original substance. As originally conceived by the Pythagoreans, the Monad is the Supreme Being, divinity or the totality of all things. According to some philosophers of the early modern period, most notably Gottfried Wilhelm Leibniz, there are infinite monads, which are the basic and immaterial elementary particles, or simplest units, that make up the universe.
In category theory, a branch of mathematics, given a morphism f: X → Y and a morphism g: Z → Y, a lift or lifting of f to Z is a morphism h: X → Z such that f = g∘h. We say that f factors through h.
In mathematics, especially in category theory, the codensity monad is a fundamental construction associating a monad to a wide class of functors.