Theorems · Theorem · category theory

HomotopicalAlgebra.RightHomotopyRel.precomp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C}
  [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] {f g : X ⟶ Y},
  HomotopicalAlgebra.RightHomotopyRel f g →
    ∀ {Z : C} (i : Z ⟶ X),
      HomotopicalAlgebra.RightHomotopyRel (CategoryTheory.CategoryStruct.comp i f)
        (CategoryTheory.CategoryStruct.comp i g)

Defined in: Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
Cited by: 0 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.PathObjectproof · cited by 32
HomotopicalAlgebra.RightHomotopyRelstatement and proof · cited by 22
HomotopicalAlgebra.PathObject.RightHomotopyproof · cited by 14
HomotopicalAlgebra.PathObject.RightHomotopy.rightHomotopyRelproof · cited by 3
HomotopicalAlgebra.PathObject.RightHomotopy.precompproof · cited by 1

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