Theorems · Definition · category theory
HomotopyEquiv.trans
{ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Preadditive V] →
{c : ComplexShape ι} →
{C D E : HomologicalComplex V c} → HomotopyEquiv C D → HomotopyEquiv D E → HomotopyEquiv C EHomotopy equivalence is a transitive relation.
- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 57 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomotopyEquiv.homproof · cited by 45
- HomotopyEquiv.invproof · cited by 31
- HomotopyEquivstatement and proof · cited by 27
- Homotopy.transproof · cited by 18
- Homotopy.compLeftproof · cited by 11
- HomotopyEquiv.homotopyInvHomIdproof · cited by 10
- HomotopyEquiv.homotopyHomInvIdproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Rep.standardComplex.forget₂ToModuleCatHomotopyEquivproof · cited by 4
- HomotopyEquiv.trans_homstatement and proof · cited by 0
- HomotopyEquiv.trans_homotopyHomInvIdstatement and proof · cited by 0
- HomotopyEquiv.trans_homotopyInvHomIdstatement and proof · cited by 0
- HomotopyEquiv.trans_invstatement and proof · cited by 0
- ChainComplex.alternatingConstHomotopyEquivproof · cited by 0