Example 2.1.5.3. Let $\operatorname{\mathcal{C}}$ be a monoidal category and let $A$ be a nonunital algebra object of $\operatorname{\mathcal{C}}$, which we identify with a nonunital lax monoidal functor $F: \{ e\} \rightarrow \operatorname{\mathcal{C}}$ as in Example 2.1.4.11. Then a map $\epsilon : \mathbf{1} \rightarrow A = F(e)$ is a unit (left unit, right unit) for $A$ (in the sense of Definition 2.1.5.1) if and only if it is a unit (left unit, right unit) for $F$ (in the sense of Definition 2.1.5.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$