 Cauchy-complete category (source code)

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= Cauchy-complete category
{c}

= Idempotent-complete
{synonym}

= Idempotent-complete category
{synonym}

A category is Cauchy-complete when every <idempotent morphism> splits: for $e:A\to A$ with $e^2=e$, there are $r:A\to B$ and $i:B\to A$ with $ir=e$ and $ri=1_B$. Its <Karoubi envelope> freely supplies these splittings. For a <small category>, this condition makes every retract of a <representable functor> representable.

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