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Remark 2.2.4.18. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $2$-categories. Every functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is unitary when viewed as a lax functor from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$. Every strict functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is strictly unitary when viewed as a lax functor from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.