Theorems · Theorem · category theory
CategoryTheory.ShortComplex.quasiIso_of_comp_right
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ S₃ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology]
[inst_4 : S₃.HasHomology] (φ : S₁ ⟶ S₂) (φ' : S₂ ⟶ S₃) [hφ' : CategoryTheory.ShortComplex.QuasiIso φ']
[hφφ' : CategoryTheory.ShortComplex.QuasiIso (CategoryTheory.CategoryStruct.comp φ φ')],
CategoryTheory.ShortComplex.QuasiIso φ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologyMapproof · cited by 83
- CategoryTheory.ShortComplex.QuasiIsostatement and proof · cited by 35
- CategoryTheory.IsIso.of_isIso_comp_rightproof · cited by 8
- CategoryTheory.ShortComplex.quasiIso_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.quasiIso_iff_comp_rightproof · cited by 0