Covariant representables are projective
= Covariant representables are projective
For a <locally small category> $\mathcal C$, every <representable functor> $\mathcal C(A,-)$ is a <projective object in a category> in $[\mathcal C,\mathbf{Set}]$. The <Yoneda lemma> identifies maps from this functor with elements at $A$, and the <pointwise epimorphism in a functor category> criterion lets such an element be lifted through any epimorphism.