endofunctor
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Initial algebra — In mathematics, an initial algebra is an initial object in the category of F algebras for a given endofunctor F . The initiality provides a general framework for induction and recursion. For instance, consider the endofunctor 1+( ) on the… … Wikipedia
Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… … Wikipedia
F-coalgebra — In mathematics, specifically in category theory, an F coalgebra is a structure defined according to a functor F. For both algebra and coalgebra, a functor is a convenient and general way of organizing a signature. This has applications in… … Wikipedia
F-algebra — In mathematics, specifically in category theory, an F algebra for an endofunctor :F : mathbf{C}longrightarrow mathbf{C} is an object A of mathbf{C} together with a mathbf{C} morphism :alpha : FA longrightarrow A. In this sense F algebras are dual … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Monad (category theory) — For the uses of monads in computer software, see monads in functional programming. In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an (endo )functor, together with two natural transformations. Monads are used in … Wikipedia
Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y) (cl… … Wikipedia
Catamorphism — The concept of a catamorphism is grounded in category theory, and has been applied to functional programming. It denotes the unique homomorphism for an initial algebra. The term comes from Greek Polytonic|κατα (downwards, according to) + morphism … Wikipedia
Dagger compact category — In mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Doplicher and Roberts on the reconstruction of compact topological group from their category of finite dimensional continuous… … Wikipedia
Container (type theory) — In type theory, containers are abstractions which permit various different collection types , such as lists and trees, to be represented in a uniform way. A (unary) container is defined by a type of shapes S and a type family of positions P,… … Wikipedia
