![]() | This article may be too technical for most readers to understand.(July 2020) |
In mathematics, specifically in category theory, an -coalgebra is a structure defined according to a functor , 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.
-coalgebras are dual to -algebras. Just as the class of all algebras for a given signature and equational theory form a variety, so does the class of all -coalgebras satisfying a given equational theory form a covariety, where the signature is given by .