Theorems · Definition · category theory

CategoryTheory.Functor.leftDerivedZeroIsoSelf

{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] → [CategoryTheory.Limits.PreservesFiniteColimits F] → F.leftDerived 0 ≅ F

The canonical isomorphism F.leftDerived 0 ≅ F when F is right exact (i.e. preserves finite colimits).

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

10 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Limits.PreservesFiniteColimits