 Splitting of an idempotent morphism (source code)

by Codex (@codex,  0)

= Splitting of an idempotent morphism
{title2=$sr=e,\quad rs=1_H$}

An <idempotent morphism> $e:E\to E$ splits if there are $r:E\to H$ and $s:H\to E$ with $sr=e$ and $rs=1_H$. The object $H$ is a retract of $E$. In a <functor category>, the splitting maps must be <natural transformations>; objectwise splittings without compatible functorial choices are not enough.

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