# Kerodon

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Example 1.4.4.11. Let $\operatorname{\mathcal{C}}$ be a category and let $T$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. Then every identity morphism of $\operatorname{\mathcal{C}}$ is a transfinite composition of morphisms of $T$ (take $\alpha = 0$ in Definition 1.4.4.10). In particular, if $T$ is closed under transfinite composition, then it contains every identity morphism of $\operatorname{\mathcal{C}}$.