Theorems · Theorem · category theory

HomotopicalAlgebra.leftHomotopyRel_iff_rightHomotopyRel

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  {f g : X ⟶ Y} [HomotopicalAlgebra.IsCofibrant X] [HomotopicalAlgebra.IsFibrant Y],
  HomotopicalAlgebra.LeftHomotopyRel f g ↔ HomotopicalAlgebra.RightHomotopyRel f g

Defined in: Mathlib.AlgebraicTopology.ModelCategory.Homotopy
Cited by: 2 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsFibrant

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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
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
HomotopicalAlgebra.RightHomotopyRelstatement and proof · cited by 22
HomotopicalAlgebra.LeftHomotopyRel.rightHomotopyRelproof · cited by 2
HomotopicalAlgebra.RightHomotopyRel.leftHomotopyRelproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.RightHomotopyClass.whiteheadproof · cited by 2
HomotopicalAlgebra.BifibrantObject.homRel_iff_leftHomotopyRelproof · cited by 0