nLab projective cover

Definition

For $N \in \mathcal{A}$ an object, a projective cover is a morphism $\tilde N \to N$ out of a projective object which is a superfluous epimorphism.

Related concepts

• projective object, projective presentation, projective cover, projective resolution

  • projective module

• injective object, injective presentation, injective envelope, injective resolution

  • injective module

• free object, free resolution

  • free module

• flat object, flat resolution

  • flat module

References

• U. Shukla, On the projective cover of a module and related results, Pacific J. Math. Volume 12, Number 2 (1962), 709-717 (Euclid)

• Wikipedia, Projective cover