Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.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}
  {h₁ : S₁.LeftHomologyData} {h₂ : S₂.LeftHomologyData} (γ : CategoryTheory.ShortComplex.LeftHomologyMapData φ h₁ h₂),
  CategoryTheory.ShortComplex.QuasiIso φ ↔ CategoryTheory.IsIso γ.φH

Defined in

Mathlib.Algebra.Homology.ShortComplex.QuasiIso

Cited by

6 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomology