Theorems · Theorem · category theory
Homotopy.ext
∀ {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} {x y : Homotopy f g}, x.hom = y.hom → x = y- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 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.coeproof · cited by 62,936
- 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 and proof · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.Hom.fproof · cited by 845
- ComplexShape.Relproof · cited by 518
- Homotopystatement and proof · cited by 106
- Homotopy.homstatement and proof · cited by 46
- prevDproof · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplex.homotopyCofiber.descSigma_ext_iffproof · cited by 0
- Homotopy.extend_ofExtendproof · cited by 0
- Homotopy.ofExtend_extendproof · cited by 0
- Homotopy.ext_iffproof · cited by 0