A reflective subcategory of a category $\mathsf{C}$ is a full subcategory $\mathsf{D}$ so that the inclusion admits a left adjoint, called the reflector or localization:\n\(\xymatrix{ \cD \ar@{^(->}@<-1ex>[r] \ar@{}[r]\mid-\perp & \mathsf{C}. \ar@<-1ex>[l]_L}\)