Example 2.2.4.10 (Algebras as Lax Functors). Let $[0]$ denote the category having a single object and a single morphism, which we regard as a (strict) $2$-category, and let $\operatorname{\mathcal{D}}$ be any $2$-category. Combining Remark 2.2.4.9 and Example 2.1.5.21, we deduce that lax functors $[0] \rightarrow \operatorname{\mathcal{D}}$ can be identified with pairs $(Y, A)$, where $Y \in \operatorname{\mathcal{D}}$ is an object and $A$ is an algebra object of the monoidal category $\underline{\operatorname{End}}_{\operatorname{\mathcal{D}}}(Y)$.

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$