= Small projective object
{title2=$\mathcal E(A,-)\text{ preserves all small colimits}$}
= 0-presentable object
{synonym}
An object with the displayed property is called small projective; the term 0-presentable here uses this all-small-colimits convention. In a <presheaf category>, every <representable presheaf> has this property by the <Yoneda lemma> and pointwise computation of <colimits>. Conversely the <canonical colimit presentation of a presheaf> shows that the identity on such an object factors through one representable, making it a retract. If the indexing category has <equalizers>, a representable retract is again representable by the <representable retract criterion>.
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