Initial Algebra

Let $F:\mathcal{C}\to \mathcal{C}$
An initial $F$-algebra is an initial object in the [[Algebra (Category Theory)|categories of $F$-algebras]].

An initial algebra is the smallest possible object that satisfies the constraints.
An arrow into an initial algebra is called a catamorphism.

Formal definition

An algebra in category theory is a set X, and a function f : F X → X
Initual if it is an initial objecect in the category of algebras
$h_0=It{f}_0$ and $hn=Itfn$
Induction ⇒ Initiality