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Theorems · Definition · category theory

HomotopicalAlgebra.PathObject.RightHomotopy.refl

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

f : X ⟶ Y is right homotopic to itself relative to any path object.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithWeakEquivalences
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HomotopicalAlgebra.RightHomotopyRel.refl · cited by 1RightHomotopyRel.reflCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomotopicalAlgebra.PathObject · cited by 32HomotopicalAlgebra.PathOb…HomotopicalAlgebra.PathObject.toPrepathObject · cited by 24PathObject.toPrepathObjectHomotopicalAlgebra.PathObject.RightHomotopy · cited by 14PathObject.RightHomotopyHomotopicalAlgebra.PrepathObject.RightHomotopy.refl · cited by 1RightHomotopy.reflRightHomotopy.reflCITED BYCITES

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Cited by1

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