Theorems · Theorem · category theory

HomotopicalAlgebra.LeftHomotopyRel.postcomp

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

Defined in: Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.Cylinderproof · cited by 31
HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
HomotopicalAlgebra.Cylinder.LeftHomotopyproof · cited by 13
HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRelproof · cited by 3
HomotopicalAlgebra.Cylinder.LeftHomotopy.postcompproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.RightHomotopyClass.whiteheadproof · cited by 2