Theorems · Definition · category theory
HomotopyCategory.subcategoryAcyclic
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] → CategoryTheory.ObjectProperty (HomotopyCategory C (ComplexShape.up ℤ))The triangulated subcategory of HomotopyCategory C (ComplexShape.up ℤ) consisting
of acyclic complexes.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upstatement and proof · cited by 1,123
- CategoryTheory.ObjectPropertystatement · cited by 798
- HomotopyCategorystatement · cited by 132
- HomotopyCategory.homologyFunctorproof · cited by 36
- CategoryTheory.Functor.homologicalKernelproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- HomotopyCategory.quasiIso_eq_trW_subcategoryAcyclicstatement and proof · cited by 2
- HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclicstatement · cited by 2
- CochainComplex.isKProjective_iff_leftOrthogonalstatement and proof · cited by 1
- HomotopyCategory.mem_subcategoryAcyclic_iffstatement · cited by 1
- HomotopyCategory.Plus.subcategoryAcyclicproof · cited by 1
- CochainComplex.IsKInjective.rightOrthogonalstatement · cited by 1
- HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAtstatement · cited by 1
- CochainComplex.isKInjective_iff_rightOrthogonalstatement and proof · cited by 1
- CochainComplex.IsKProjective.leftOrthogonalstatement · cited by 1
- HomotopyCategory.Plus.quasiIso_eq_subcategoryAcyclic_trWproof · cited by 0
- HomotopyCategory.quasiIso_eq_subcategoryAcyclic_Wstatement · cited by 0