In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature.
F-algebras can also be used to represent data structures used in programming, such as lists and trees.
The main related concepts are initial F-algebras which may serve to encapsulate the induction principle, and the dual construction F-coalgebras.