Corollary 8.5.2.6. Let $\operatorname{\mathcal{C}}$ be a category which admits equalizers (or coequalizers). Then every idempotent endomorphism in $\operatorname{\mathcal{C}}$ is split.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 8.5.2.6. Let $\operatorname{\mathcal{C}}$ be a category which admits equalizers (or coequalizers). Then every idempotent endomorphism in $\operatorname{\mathcal{C}}$ is split.