High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In 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 {C} be a category and X an object in {C}. A projective cover is a pair (P,p), with P a projective object in {C} and p a superfluous epimorphism f in Hom(P, X). In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions respectively to objects linked in diagrams by morphisms or arrows.

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