Remark 2.1.6.2. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be monoidal categories. We will generally abuse terminology by identifying a monoidal functor $(F,\mu )$ from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$ with the underlying functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$. If we refer to $F$ as a monoidal functor, we implicitly assume that it has been equipped with a monoidal structure $\mu = \{ \mu _{X,Y} \} _{X,Y \in \operatorname{\mathcal{C}}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$