Theorems · Theorem · category theory
CategoryTheory.ShortComplex.quasiIso_iff_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'],
CategoryTheory.ShortComplex.QuasiIso (CategoryTheory.CategoryStruct.comp φ φ') ↔
CategoryTheory.ShortComplex.QuasiIso φ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
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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.QuasiIsostatement and proof · cited by 35
- CategoryTheory.ShortComplex.quasiIso_of_comp_rightproof · cited by 1
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