Theorems · Theorem · category theory

HomologicalComplex.quasiIso_truncGEMap_iff

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {K L : HomologicalComplex C c'} (φ : K ⟶ L) (e : c.Embedding c') [inst_2 : e.IsTruncGE]
  [inst_3 : ∀ (i' : ι'), K.HasHomology i'] [inst_4 : ∀ (i' : ι'), L.HasHomology i']
  [inst_5 : CategoryTheory.Limits.HasZeroObject C],
  QuasiIso (HomologicalComplex.truncGEMap φ e) ↔ ∀ (i : ι) (i' : ι'), e.f i = i' → QuasiIsoAt φ i'

Defined in

Mathlib.Algebra.Homology.Embedding.TruncGEHomology

Cited by

2 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsComplexShape.Embedding.IsTruncGEHomologicalComplex.HasHomologyHomologicalComplex.HasHomologyCategoryTheory.Limits.HasZeroObject