Indecomposable projective object
= Indecomposable projective object
An object is indecomposable projective if every epic map from a coproduct to it has a component which is split epic. In a <presheaf category>, representables have this property by evaluation of the identity. Conversely the canonical representable cover shows such an object is a retract of a representable; if idempotents split in the indexing category, it is itself representable.