Theorems · Theorem · category theory

CategoryTheory.Functor.isZero_leftDerived_obj_projective_succ

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.HasProjectiveResolutions C]
  [inst_4 : CategoryTheory.Abelian D] (F : CategoryTheory.Functor C D) [inst_5 : F.Additive] (n : ℕ) (X : C)
  [CategoryTheory.Projective X], CategoryTheory.Limits.IsZero ((F.leftDerived (n + 1)).obj X)

The higher derived functors vanish on projective objects.

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

3 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Projective