Theorems · Theorem · category theory
CategoryTheory.ShortComplex.quasiIso_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology] (φ : S₁ ⟶ S₂),
CategoryTheory.ShortComplex.QuasiIso φ ↔ CategoryTheory.IsIso (CategoryTheory.ShortComplex.homologyMap φ)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologystatement · cited by 216
- CategoryTheory.ShortComplex.homologyMapstatement and proof · cited by 83
- CategoryTheory.ShortComplex.QuasiIsostatement and proof · cited by 35
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_iffproof · cited by 6
- quasiIsoAt_iff_isIso_homologyMapproof · cited by 6
- CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_iffproof · cited by 6
- CategoryTheory.ShortComplex.quasiIso_of_comp_leftproof · cited by 1
- CategoryTheory.ShortComplex.quasiIso_of_comp_rightproof · cited by 1
- CategoryTheory.ShortComplex.quasiIso_of_retractproof · cited by 1
- CategoryTheory.ShortComplex.quasiIso_iff_evaluationproof · cited by 0