Theorems · Definition · category theory
CochainComplex.HomComplex.Cochain.ofHomotopy
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{F G : CochainComplex C ℤ} → {φ₁ φ₂ : F ⟶ G} → Homotopy φ₁ φ₂ → CochainComplex.HomComplex.Cochain F G (-1)The cochain of degree -1 given by a homotopy between two morphisms of complexes.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 32,603
- 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
- Homotopystatement and proof · cited by 106
- Homotopy.homproof · cited by 46
- CochainComplex.HomComplex.Cochain.mkproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cochain.equivHomotopyproof · cited by 8
- CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coestatement · cited by 2
- CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂proof · cited by 1
- CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃proof · cited by 1
- CochainComplex.HomComplex.Cochain.ofHomotopy_reflstatement · cited by 0
- CochainComplex.HomComplex.δ_ofHomotopystatement and proof · cited by 0
- CochainComplex.HomComplex.Cochain.ofHomotopy_ofEqstatement · cited by 0