Kerodon

Example 6.1.1.2. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ be functors between categories, which we regard as $1$-morphisms in the strict $2$-category $\mathbf{Cat}$ of Example 2.2.0.4. An adjunction between $F$ and $G$ in the $2$-category $\mathbf{Cat}$ is an adjunction between $F$ and $G$ in the usual category-theoretic sense: that is, a pair of natural transformations $\eta : \operatorname{id}_{\operatorname{\mathcal{C}}} \rightarrow G \circ F$ and $\epsilon : F \circ G \rightarrow \operatorname{id}_{\operatorname{\mathcal{D}}}$ which satisfy the requirements of Definition 6.1.0.2.