Theorems · Theorem · category theory

HomotopicalAlgebra.LeftHomotopyRel.trans

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {f₀ f₁ f₂ : X ⟶ Y} [HomotopicalAlgebra.IsCofibrant X],
  HomotopicalAlgebra.LeftHomotopyRel f₀ f₁ →
    HomotopicalAlgebra.LeftHomotopyRel f₁ f₂ → HomotopicalAlgebra.LeftHomotopyRel f₀ f₂

Defined in: Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory HomotopicalAlgebra.IsCofibrant

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Cites11

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.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
HomotopicalAlgebra.Cylinderproof · cited by 31
HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
HomotopicalAlgebra.Cylinder.LeftHomotopyproof · cited by 13
HomotopicalAlgebra.Cylinder.IsGoodproof · cited by 11
HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinderproof · cited by 3
HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRelproof · cited by 3
HomotopicalAlgebra.Cylinder.LeftHomotopy.transproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.LeftHomotopyRel.equivalenceproof · cited by 2