Projective envelope

In the branch of abstract mathematics called category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P. Projective covers are the dual of injective envelopes.

Let ${\displaystyle {\mathcal {C}}}$ be a category and X an object in ${\displaystyle {\mathcal {C}}}$. A projective cover is a pair (P,p), with P a projective object in ${\displaystyle {\mathcal {C}}}$ and p a superfluous epimorphism in Hom(P, X).

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