Theorems · Definition · category theory
HomotopyEquiv.inv
{ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Preadditive V] →
{c : ComplexShape ι} → {C D : HomologicalComplex V c} → HomotopyEquiv C D → (D ⟶ C)The backward chain map
- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Homstatement · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomotopyEquivstatement and proof · cited by 27
Cited by39
Results whose statement or proof uses this declaration.
- HomotopyEquiv.homotopyInvHomIdstatement · cited by 10
- HomotopyEquiv.homotopyHomInvIdstatement · cited by 8
- HomotopyEquiv.symmproof · cited by 5
- HomotopyEquiv.transproof · cited by 4
- HomotopyCategory.isoOfHomotopyEquivproof · cited by 4
- CategoryTheory.Functor.mapHomotopyEquivproof · cited by 4
- HomotopyEquiv.copyproof · cited by 3
- CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_πstatement · cited by 2
- CochainComplex.mappingConeCompHomotopyEquiv_comm₁statement · cited by 2
- CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_idstatement · cited by 2
- CategoryTheory.ProjectiveResolution.iso_inv_naturalityproof · cited by 2
- CochainComplex.mappingConeCompTriangleh_comm₁proof · cited by 2