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Theorems · Definition · category theory

HomotopicalAlgebra.BifibrantObject.homRel

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] → HomRel (HomotopicalAlgebra.BifibrantObject C)

The homotopy relation on the category of bifibrant objects.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by
22 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopicalAlgebra.BifibrantObject.HoCat · cited by 20BifibrantObject.HoCatHomotopicalAlgebra.BifibrantObject.toHoCat · cited by 20BifibrantObject.toHoCatHomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject · cited by 6HoCat.ιCofibrantObjectHomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution · cited by 5HoCat.bifibrantResolutionHomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight · cited by 4HoCat.homEquivRightHomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution' · cited by 2HoCat.bifibrantResolution'HomotopicalAlgebra.BifibrantObject.homRel_iff_rightHomotopyRel · cited by 2BifibrantObject.homRel_if…HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObject · cited by 2HoCat.ιFibrantObjectHomotopicalAlgebra.CofibrantObject.HoCat.adjCounit' · cited by 1HoCat.adjCounit'HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso · cited by 1HoCat.adjCounitIsoHomotopicalAlgebra.CofibrantObject.HoCat.adjUnit · cited by 1HoCat.adjUnitHomotopicalAlgebra.BifibrantObject.toHoCat_map_eq_iff · cited by 1BifibrantObject.toHoCat_m…HomotopicalAlgebra.BifibrantObject.toHoCat_obj_surjective · cited by 1BifibrantObject.toHoCat_o…HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft · cited by 1HoCat.homEquivLeftHomotopicalAlgebra.CofibrantObject.HoCat.adj · cited by 0HoCat.adjCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…HomRel · cited by 49HomRelHomotopicalAlgebra.BifibrantObject · cited by 38HomotopicalAlgebra.Bifibr…HomotopicalAlgebra.bifibrantObjects · cited by 37HomotopicalAlgebra.bifibr…HomotopicalAlgebra.RightHomotopyRel · cited by 22HomotopicalAlgebra.RightH…BifibrantObject.homRelCITED BYCITES

Cites9

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Cited by37

Results whose statement or proof uses this declaration.