Theorems · Theorem · category theory

HomologicalComplex.quasiIso_extendMap_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]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {K L : HomologicalComplex C c} (φ : K ⟶ L) (e : c.Embedding c')
  [inst_3 : ∀ (j : ι), K.HasHomology j] [inst_4 : ∀ (j : ι), L.HasHomology j],
  QuasiIso (HomologicalComplex.extendMap φ e) ↔ QuasiIso φ

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomology

Cited by

2 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectHomologicalComplex.HasHomologyHomologicalComplex.HasHomology