Theorems · Theorem · category theory

CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_assoc

∀ {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]
  [inst_6 : CategoryTheory.Limits.PreservesFiniteColimits F] {Z : CategoryTheory.Functor C D} (h : F ⟶ Z),
  CategoryTheory.CategoryStruct.comp F.leftDerivedZeroIsoSelf.inv
      (CategoryTheory.CategoryStruct.comp F.fromLeftDerivedZero h) =
    h

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

0 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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