# Kerodon

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

Remark 2.1.2.2. Let $\operatorname{\mathcal{C}}$ be a nonunital strict monoidal category. We will say that an object $\mathbf{1} \in \operatorname{\mathcal{C}}$ is a strict unit if it satisfies condition $(\ast )$ of Definition 2.1.2.1. Note that if such an object exists, then it is uniquely determined: it can be characterized as the unit element of the monoid $\operatorname{Ob}(\operatorname{\mathcal{C}})$.