Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.desc_commutes_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {Y Z : C} (f : Z ⟶ Y)
  (I : CategoryTheory.InjectiveResolution Y) (J : CategoryTheory.InjectiveResolution Z),
  CategoryTheory.CategoryStruct.comp (J.ι.f 0) ((CategoryTheory.InjectiveResolution.desc f I J).f 0) =
    CategoryTheory.CategoryStruct.comp f (I.ι.f 0)

Defined in: Mathlib.CategoryTheory.Abelian.Injective.Resolution
Cited by: 2 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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Cites17

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
HomologicalComplex.Xstatement · cited by 1,839
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
HomologicalComplex.Hom.fstatement and proof · cited by 845
CategoryTheory.InjectiveResolutionstatement and proof · cited by 90
CategoryTheory.InjectiveResolution.cocomplexstatement · cited by 73
CochainComplex.single₀statement · cited by 59

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.InjectiveResolution.desc_commutes_zero_assocproof · cited by 0
CategoryTheory.InjectiveResolution.toRightDerivedZero_eqproof · cited by 0