What is "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 computer science: examples of coalgebras include lazy, infinite data structures, such as streams, and also transition systems.

F-coalgebras are dual to 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 F-coalgebras satisfying a given equational theory form a covariety, where the signature is given by F.