Theorems · Definition · category theory

HomotopicalAlgebra.PathObject.RightHomotopy.symm

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] →
        {P : HomotopicalAlgebra.PathObject Y} → {f g : X ⟶ Y} → P.RightHomotopy f g → P.symm.RightHomotopy g f

If f and g are homotopic relative to a path object P, then g and f are homotopic relative to P.symm.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 13 from the axioms · uses propext
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

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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
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.PathObjectstatement and proof · cited by 32
HomotopicalAlgebra.PathObject.RightHomotopystatement and proof · cited by 14
HomotopicalAlgebra.PathObject.symmstatement · cited by 6
HomotopicalAlgebra.PrepathObject.RightHomotopy.symmproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.RightHomotopyRel.symmproof · cited by 1