Theorems · Definition · category theory
Homotopy.hom
{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} → {f g : C ⟶ D} → Homotopy f g → (i j : ι) → C.X i ⟶ D.X j- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 46 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.
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- Homotopystatement and proof · cited by 106
Cited by68
Results whose statement or proof uses this declaration.
- Homotopy.transproof · cited by 18
- HomologicalComplex.homotopyCofiber.descproof · cited by 15
- Homotopy.compLeftproof · cited by 11
- CochainComplex.HomComplex.Cochain.ofHomotopyproof · cited by 6
- HomologicalComplex.mapBifunctorMapHomotopy.hom₁proof · cited by 5
- Homotopy.zerostatement · cited by 5
- Homotopy.compRightproof · cited by 4
- Homotopy.extstatement and proof · cited by 4
- Homotopy.extendproof · cited by 4
- Homotopy.ofExtendproof · cited by 4
- HomologicalComplex.homotopyCofiber.inrCompHomotopy_homstatement · cited by 4
- HomologicalComplex.homotopyCofiber.inrX_desc_fproof · cited by 4