Theorems · Theorem · category theory
HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinder
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : HomotopicalAlgebra.ModelCategory C]
{f g : X ⟶ Y}, HomotopicalAlgebra.LeftHomotopyRel f g → ∃ P, P.IsGood ∧ Nonempty (P.LeftHomotopy f g)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.pairstatement · cited by 536
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.Cylinderstatement and proof · cited by 31
- HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
- HomotopicalAlgebra.Cylinder.LeftHomotopystatement and proof · cited by 13
- HomotopicalAlgebra.Cylinder.IsGoodstatement · cited by 11
- HomotopicalAlgebra.Cylinder.LeftHomotopy.exists_good_cylinderproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinderproof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.rightHomotopyproof · cited by 1
- HomotopicalAlgebra.LeftHomotopyRel.transproof · cited by 1