Theorems · Definition · category theory

HomotopyEquiv.symm

{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} → HomotopyEquiv C D → HomotopyEquiv D C

Being homotopy equivalent is a symmetric relation.

Defined in: Mathlib.Algebra.Homology.Homotopy
Cited by: 5 results in Mathlib
Foundations: Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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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
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
HomotopyEquiv.homotopyInvHomIdproof · cited by 10
HomotopyEquiv.homotopyHomInvIdproof · cited by 8

Cited by5

Results whose statement or proof uses this declaration.

HomotopyEquiv.symm_homstatement and proof · cited by 0
HomotopyEquiv.symm_homotopyHomInvIdstatement and proof · cited by 0
HomotopyEquiv.symm_homotopyInvHomIdstatement and proof · cited by 0
HomotopyEquiv.symm_invstatement and proof · cited by 0
HomotopyEquiv.homotopyEquivalences_invproof · cited by 0