$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example (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 and Example, 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 $\underline{\operatorname{End}}_{\operatorname{\mathcal{D}}}(Y)$.