Theorems · Theorem · category theory

HomologicalComplex.acyclic_truncGE_iff_isSupportedOutside

∀ {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 : HomologicalComplex C c') (e : c.Embedding c') [inst_2 : e.IsTruncGE] [inst_3 : ∀ (i' : ι'), K.HasHomology i']
  [inst_4 : CategoryTheory.Limits.HasZeroObject C], (K.truncGE e).Acyclic ↔ K.IsSupportedOutside e

Defined in

Mathlib.Algebra.Homology.Embedding.TruncGEHomology

Cited by

3 results in Mathlib

Foundations

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

Assumes

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