Theorems · Inductive type · category theory

CategoryTheory.ShortComplex.QuasiIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} → [S₁.HasHomology] → [S₂.HasHomology] → (S₁ ⟶ S₂) → Prop

A morphism φ : S₁ ⟶ S₂ of short complexes that have homology is a quasi-isomorphism if the induced map homologyMap φ : S₁.homology ⟶ S₂.homology is an isomorphism.

Defined in

Mathlib.Algebra.Homology.ShortComplex.QuasiIso

Cited by

35 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

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