Kerodon

Remark 2.2.0.2 (Strict $2$-Categories as Enriched Categories). Let $\operatorname{Cat}$ denote the category whose objects are (small) categories and whose morphisms are functors. Then $\operatorname{Cat}$ admits finite products, and therefore admits a monoidal structure given by the formation of cartesian products (Example 2.1.3.2). Neglecting set-theoretic technicalities, a strict $2$-category (in the sense of Definition 2.2.0.1) can be identified with a $\operatorname{Cat}$-enriched category (in the sense of Definition 2.1.7.1).