Theorems · Definition · category theory
CategoryTheory.InjectiveResolution.descHomotopyZeroZero
{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 : I.cocomplex ⟶ J.cocomplex) →
CategoryTheory.CategoryStruct.comp I.ι f = 0 → (I.cocomplex.X 1 ⟶ J.cocomplex.X 0)An auxiliary definition for descHomotopyZero.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.fproof · cited by 845
- CategoryTheory.InjectiveResolutionstatement and proof · cited by 90
- CategoryTheory.InjectiveResolution.cocomplexstatement and proof · cited by 73
- CochainComplex.single₀statement · cited by 59
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.InjectiveResolution.descHomotopyZeroOneproof · cited by 3
- CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOnestatement and proof · cited by 1
- CategoryTheory.InjectiveResolution.comp_descHomotopyZeroZerostatement · cited by 1
- CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOne_assocstatement and proof · cited by 0
- CategoryTheory.InjectiveResolution.comp_descHomotopyZeroZero_assocstatement and proof · cited by 0
- CategoryTheory.InjectiveResolution.descHomotopyZeroproof · cited by 0
- CategoryTheory.InjectiveResolution.descHomotopyZeroZero.congr_simpstatement and proof · cited by 0