Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.of

{C : Type u_1} →
  [inst : CategoryTheory.Category.{u_2, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [CategoryTheory.EnoughProjectives C] → (Z : C) → CategoryTheory.ProjectiveResolution Z

In any abelian category with enough projectives, ProjectiveResolution.of Z constructs a projective resolution of the object Z.

Defined in: Mathlib.CategoryTheory.Abelian.Projective.Resolution
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.EnoughProjectives

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement · cited by 32,673
CategoryTheory.Abelianstatement · cited by 1,753
CategoryTheory.ProjectiveResolutionstatement · cited by 92
CategoryTheory.EnoughProjectivesstatement · cited by 13

Cited by1

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CategoryTheory.ProjectiveResolution.of_defstatement · cited by 0