Example 2.2.1.4 (Strict $2$-Categories). Let $\operatorname{\mathcal{C}}$ be any strict $2$-category (in the sense of Definition 2.2.0.1). Then $\operatorname{\mathcal{C}}$ can be viewed as a $2$-category (in the sense of Definition 2.2.1.1) by taking the unit and associativity constraints $\upsilon _{X}$ and $\alpha _{h,g,f}$ to be identity $2$-morphisms in $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$