Theorems · Theorem · category theory
CategoryTheory.ShortComplex.quasiIso_of_arrow_mk_iso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ S₃ S₄ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology]
[inst_4 : S₃.HasHomology] [inst_5 : S₄.HasHomology] (φ : S₁ ⟶ S₂) (φ' : S₃ ⟶ S₄)
(e : CategoryTheory.Arrow.mk φ ≅ CategoryTheory.Arrow.mk φ') [hφ : CategoryTheory.ShortComplex.QuasiIso φ],
CategoryTheory.ShortComplex.QuasiIso φ'- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Arrow.mkstatement and proof · cited by 421
- CategoryTheory.Iso.inv_hom_idproof · cited by 308
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.quasiIso_iff_of_arrow_mk_isoproof · cited by 1