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Theorems · Theorem · category theory

HomotopicalAlgebra.Cylinder.LeftHomotopy.exists_good_cylinder

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {P : HomotopicalAlgebra.Cylinder X} {f g : X ⟶ Y} (h : P.LeftHomotopy f g),
  ∃ P', P'.IsGood ∧ Nonempty (P'.LeftHomotopy f g)
Defined in
Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by
1 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory
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HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinder · cited by 3LeftHomotopyRel.exists_go…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.coprod · cited by 252Limits.coprodHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…CategoryTheory.Limits.coprod.inl · cited by 137coprod.inlCategoryTheory.Limits.coprod.inr · cited by 132coprod.inrHomotopicalAlgebra.Precylinder.I · cited by 75Precylinder.ICategoryTheory.MorphismProperty.MapFactorizationData.Z · cited by 63MapFactorizationData.ZCategoryTheory.MorphismProperty.MapFactorizationData · cited by 63MorphismProperty.MapFacto…LeftHomotopy.exists_good_cyli…CITED BYCITES

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