Category

Projective object

Let be a category. An object is said to be projective iff it has the following (left) lifting property against epimorphisms: For any morphism and epimorphism , there exists a factorization so that . #m/def/cat

Equivalently, the covariant hom-functor preserves epimorphisms.

See also

• Projective module, the original case.
• Injective object, the dual notion.

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