Theorems · Theorem · category theory
HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinder
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : HomotopicalAlgebra.ModelCategory C]
{f g : X ⟶ Y} [HomotopicalAlgebra.IsFibrant Y],
HomotopicalAlgebra.LeftHomotopyRel f g → ∃ P, P.IsVeryGood ∧ Nonempty (P.LeftHomotopy f g)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
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.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.pairstatement · cited by 536
- CategoryTheory.Limits.coprodproof · cited by 252
- CategoryTheory.CommSqproof · cited by 158
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- CategoryTheory.Limits.terminal.fromproof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.FibrantObject.factorsThroughLocalizationproof · cited by 0
- HomotopicalAlgebra.LeftHomotopyRel.precompproof · cited by 0