Free Algebra

Definition

Let $\mathcal{C}$ be a category with coproducts. Let $F:\mathcal{C}\Rightarrow \mathcal{C}$ be an endofunctors. Let $A:\mathcal{C}$ be an object. Say $X$ is the free $F$-Algebra (Category Theory) on $A$. Specifically, it is the initial algebra over the endofunctor $F(-)+A$.