Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.descHomotopyZeroZero.congr_simp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {Y Z : C}
  {I : CategoryTheory.InjectiveResolution Y} {J : CategoryTheory.InjectiveResolution Z}
  (f f_1 : I.cocomplex ⟶ J.cocomplex) (e_f : f = f_1) (comm : CategoryTheory.CategoryStruct.comp I.ι f = 0),
  CategoryTheory.InjectiveResolution.descHomotopyZeroZero f comm =
    CategoryTheory.InjectiveResolution.descHomotopyZeroZero f_1 ⋯

Defined in: Mathlib.CategoryTheory.Abelian.Injective.Resolution
Cited by: 0 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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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
CategoryTheory.InjectiveResolutionstatement and proof · cited by 90
CategoryTheory.InjectiveResolution.cocomplexstatement and proof · cited by 73
CochainComplex.single₀statement · cited by 59
CategoryTheory.InjectiveResolution.ιstatement and proof · cited by 48

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