Theorems · Theorem · category theory
homotopyEquivalences_le_quasiIso
∀ {ι : Type u_1} (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
(c : ComplexShape ι) [inst_2 : CategoryTheory.CategoryWithHomology C],
HomologicalComplex.homotopyEquivalences C c ≤ HomologicalComplex.quasiIso C c- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- HomotopyEquiv.homproof · cited by 45
- HomologicalComplex.quasiIsostatement · cited by 42
- HomotopyEquivproof · cited by 27
- HomologicalComplex.homotopyEquivalencesstatement and proof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- CochainComplex.IsKInjective.quasiIso_iffproof · cited by 2
- CochainComplex.IsKProjective.quasiIso_iffproof · cited by 1
- ComplexShape.QFactorsThroughHomotopy_of_exists_prevproof · cited by 0
- HomologicalComplexUpToQuasiIso.Q_inverts_homotopyEquivalencesproof · cited by 0