Example 6.1.2.2. Let $\operatorname{\mathcal{C}}$ be a $2$-category containing $1$-morphisms $f: C \rightarrow D$ and $g: D \rightarrow C$. Then:
Every $2$-morphism $\eta : \operatorname{id}_{C} \Rightarrow g \circ f$ is equal to the right adjunct of the right unit constraint $\rho _{f}: f \circ \operatorname{id}_{D} \xRightarrow {\sim } f$ (with respect to $\eta $).
Every $2$-morphism $\epsilon : f \circ g \Rightarrow \operatorname{id}_{D}$ is equal to the left adjunct of $\rho _{g}^{-1}: g \xRightarrow {\sim } g \circ \operatorname{id}_{D}$ (with respect to $\epsilon $).