# Kerodon

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Definition 2.2.7.1. Let $\operatorname{\mathcal{C}}$ be a $2$-category. We will say that $\operatorname{\mathcal{C}}$ is strictly unitary if, for each $1$-morphism $f: X \rightarrow Y$ in $\operatorname{\mathcal{C}}$, the left and right unit constraints

$\lambda _{f}: \operatorname{id}_{Y} \circ f \xRightarrow {\sim } f \quad \quad \rho _{f}: f \circ \operatorname{id}_{X} \xRightarrow {\sim } f$

are identity $2$-morphisms of $\operatorname{\mathcal{C}}$.