Theorems · Theorem · category theory

HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRel

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C]
  {X Y : C} {f g : X ⟶ Y} {P : HomotopicalAlgebra.Cylinder X} (h : P.LeftHomotopy f g),
  HomotopicalAlgebra.LeftHomotopyRel f g

Defined in: Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by: 3 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithWeakEquivalences

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Cites6

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.Cylinderstatement and proof · cited by 31
HomotopicalAlgebra.LeftHomotopyRelstatement · cited by 22
HomotopicalAlgebra.Cylinder.LeftHomotopystatement and proof · cited by 13

Cited by3

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.LeftHomotopyRel.symmproof · cited by 1
HomotopicalAlgebra.LeftHomotopyRel.transproof · cited by 1
HomotopicalAlgebra.LeftHomotopyRel.postcompproof · cited by 1