Use 0-presentable object in the specified sense: its hom-functor preserves all small colimits. For a representable , the Yoneda lemma identifies this hom-functor with evaluation at . Given any small diagram , pointwise colimits give
(1)
These are the canonical comparison bijections, including for an empty diagram. Therefore every representable presheaf is 0-presentable, or a small projective object in this sense.

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