Coproducts of projective objects are projective
= Coproducts of projective objects are projective
A set-indexed <coproduct in a category> of <projective objects in a category> is projective. Restrict a map out of the coproduct to each summand, lift each restriction through the given <epimorphism>, and assemble the lifts by the coproduct universal property. Choosing an arbitrary family of lifts uses the usual <axiom of choice>. The empty coproduct, an <initial object>, is projective as well.