: Matemáticas: F-coalgebra

category theory > F-coalgebra

F-coalgebra

In mathematics, specifically in category theory, an ${\\displaystyle F}$ -coalgebra is a structure defined according to a functor ${\\displaystyle F}$ , with specific properties as defined below. For both algebras and coalgebras, a functor is a convenient and general way of organizing a signature. This has applications in computer science: examples of coalgebras include lazy evaluation, infinite data structures, such as streams, and also transition systems. ${\\displaystyle F}$ -coalgebras are dual to ${\\displaystyle F}$ -algebras. Just as the class of all algebras for a given signature and equational theory form a variety, so does the class of all ${\\displaystyle F}$ -coalgebras satisfying a given equational theory form a covariety, where the signature is given by ${\\displaystyle F}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/F-coalgebra)

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