Warning 1.3.7.10. Definitions 1.3.7.7 and 1.3.7.8 are not invariant under equivalence of categories. If $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is an equivalence of categories and $\operatorname{\mathcal{C}}$ is free, then $\operatorname{\mathcal{D}}$ need not be free; if $f$ is an indecomposable morphism in $\operatorname{\mathcal{C}}$, then $F(f)$ need not be an indecomposable morphism of $\operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$