# Kerodon

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Definition 1.2.6.8. Let $\operatorname{\mathcal{C}}$ be a category. We will say that a morphism $f: X \rightarrow Y$ in $\operatorname{\mathcal{C}}$ is indecomposable if $f$ is not an identity morphism, and for every factorization $f = g \circ h$ have either $g = \operatorname{id}_{Y}$ (so $h=f$) or $h = \operatorname{id}_{X}$ (so $g=f$).