CatDat

Implication Details

Assumptions: reflector

Conclusions: left adjoint, right-invertible

Proof: If $F : \C \to \D$ is a reflector, it is left adjoint to a fully faithful functor $G : \D \to \C$. Thus, the counit $\varepsilon : F \circ G \to \id_{\D}$ is an isomorphism (Prop. 3.4 at the nLab). This shows that $G$ is a right inverse of $F$.