<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math>F -algebra (algebra for an endofunctor)

With a proper category $C$ which can encode the signature of $F(-)$ , and an [endofunctor](math-001T) $F : C \to C$ , the $F$ -algebra is a triple:

(F, x, \alpha)

where $\alpha : F \; x \to x$ is a $C$ -morphism.