Theorems · Inductive type · category theory

QuasiIsoAt

{ι : Type u_1} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {c : ComplexShape ι} →
          {K L : HomologicalComplex C c} → (K ⟶ L) → (i : ι) → [K.HasHomology i] → [L.HasHomology i] → Prop

A morphism of homological complexes f : K ⟶ L is a quasi-isomorphism in degree i when it induces a quasi-isomorphism of short complexes K.sc i ⟶ L.sc i.

Defined in

Mathlib.Algebra.Homology.QuasiIso

Cited by

55 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology