F-coalgebra

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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,^{[clarification needed]} 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 ${\displaystyle F}$.