Theorems · Theorem · category theory

CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app

∀ {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] (X : C),
  CategoryTheory.CategoryStruct.comp (F.fromLeftDerivedZero.app X) (F.leftDerivedZeroIsoSelf.inv.app X) =
    CategoryTheory.CategoryStruct.id ((F.leftDerived 0).obj X)

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

1 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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