Theorems · Theorem · category theory

CategoryTheory.ShortComplex.quasiIso_of_retract

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ T₁ S₂ T₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : T₁.HasHomology]
  [inst_4 : S₂.HasHomology] [inst_5 : T₂.HasHomology] {f₁ : S₁ ⟶ T₁} {f₂ : S₂ ⟶ T₂}
  (h : CategoryTheory.RetractArrow f₁ f₂) [hf₂ : CategoryTheory.ShortComplex.QuasiIso f₂],
  CategoryTheory.ShortComplex.QuasiIso f₁

Defined in

Mathlib.Algebra.Homology.ShortComplex.Retract

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.QuasiIso