 Triangle identities for an adjunction

For $F⊣G$ with adjunction unit $\eta$ and adjunction counit $\epsilon$, the identities are ${\epsilon }_{FC}F{\eta }_C=1_{FC}$ and $G{\epsilon }_D{\eta }_{GD}=1_{GD}$. They make the transpose maps $f\mapsto Gf\eta$ and $g\mapsto \epsilon Fg$ inverse.