 Reflective subcategory

A full subcategory $\mathcal{D}\subseteq \mathcal{C}$ is reflective when its inclusion has a left adjoint $L:\mathcal{C}\to \mathcal{D}$, called the reflector. Equivalently, every object $A$ has a universal morphism $A\to LA$ into an object of $\mathcal{D}$.