Free Sigma 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 on $A$. Specifically, it is the initial algebra over the endofunctor $F(-)+A$.