Kerodon

Example 2.1.7.12. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be small categories, which we regard as $\operatorname{Set}$-enriched categories by means of Example 2.1.7.2. Then $\operatorname{Set}$-enriched functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$ (in the sense of Definition 2.1.7.10) can be identified with functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$ in the usual sense. This identification determines an isomorphism of categories $\operatorname{Cat}\simeq \operatorname{Cat}(\operatorname{Set})$.