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Theorems · Theorem · category theory

HomotopicalAlgebra.BifibrantObject.homRel_iff_rightHomotopyRel

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {X Y : HomotopicalAlgebra.BifibrantObject C} {f g : X ⟶ Y},
  HomotopicalAlgebra.BifibrantObject.homRel C f g ↔ HomotopicalAlgebra.RightHomotopyRel f.hom g.hom
Defined in
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by
2 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory
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Around this declaration

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HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObj_hom_ext · cited by 0CofibrantObject.bifibrant…HomotopicalAlgebra.BifibrantObject.homRel_iff_leftHomotopyRel · cited by 0BifibrantObject.homRel_if…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…HomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…HomotopicalAlgebra.BifibrantObject · cited by 38HomotopicalAlgebra.Bifibr…HomotopicalAlgebra.bifibrantObjects · cited by 37HomotopicalAlgebra.bifibr…HomotopicalAlgebra.RightHomotopyRel · cited by 22HomotopicalAlgebra.RightH…HomotopicalAlgebra.BifibrantObject.homRel · cited by 22BifibrantObject.homRelBifibrantObject.homRel_iff_ri…CITED BYCITES

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