 Functor-split coequalizer pair

For $G:\mathcal{D}\to \mathcal{C}$, a parallel pair in $\mathcal{D}$ is G-split if its image admits a split coequalizer in $\mathcal{C}$. Reflection of such coequalizers means that an existing equalizing arrow in $\mathcal{D}$ is a coequalizer whenever its image is the corresponding split coequalizer. This asserts a property of existing arrows; it does not assert that a lift exists for every base quotient.