Theorems · Theorem · category theory
CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G : CochainComplex C ℤ} (φ₁ φ₂ : F ⟶ G) (ho : Homotopy φ₁ φ₂),
↑((CochainComplex.HomComplex.Cochain.equivHomotopy φ₁ φ₂) ho) = CochainComplex.HomComplex.Cochain.ofHomotopy ho- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Equivstatement · cited by 8,337
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainstatement · cited by 341
- CochainComplex.HomComplex.Cochain.ofHomstatement · cited by 121
- Homotopystatement and proof · cited by 106
- CochainComplex.HomComplex.δstatement · cited by 102
- CochainComplex.HomComplex.Cochain.equivHomotopystatement and proof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂proof · cited by 1
- CochainComplex.mappingCone.map_eq_mapOfHomotopyproof · cited by 0