An adjunction consists of a pair of functors $F \colon \mathsf{C} \to \mathsf{D}$ and $G \colon \mathsf{D} \to \mathsf{C}$ together with an isomorphism \(\mathsf{D}(Fc,d) \cong \mathsf{C}(c,Gd)\) for each $c \in \mathsf{C}$ and $d \in \mathsf{D}$ that is natural in both variables. Here $F$ is left adjoint to $G$ and $G$ is right adjoint to $F$. The morphisms \(\xymatrix{ Fc \ar[r]^{f^\sharp} & d} \qquad \leftrightsquigarrow\qquad \xymatrix{ c \ar[r]^{f^\flat} & Gd}\) corresponding under the bijection \eqref{eq:hom-set-adj} are adjunct or are transposes of each other.