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.
- Cited by
- 22 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.
Cites9
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.Homproof · cited by 32,603
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomRelstatement · cited by 49
- HomotopicalAlgebra.BifibrantObjectstatement and proof · cited by 38
- HomotopicalAlgebra.bifibrantObjectsstatement · cited by 37
- HomotopicalAlgebra.RightHomotopyRelproof · cited by 22
Cited by37
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.BifibrantObject.HoCatproof · cited by 20
- HomotopicalAlgebra.BifibrantObject.toHoCatstatement and proof · cited by 20
- HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObjectstatement and proof · cited by 6
- HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolutionstatement · cited by 5
- HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRightstatement and proof · cited by 4
- HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'statement · cited by 2
- HomotopicalAlgebra.BifibrantObject.homRel_iff_rightHomotopyRelstatement · cited by 2
- HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObjectstatement and proof · cited by 2
- HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'statement and proof · cited by 1
- HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIsostatement · cited by 1
- HomotopicalAlgebra.CofibrantObject.HoCat.adjUnitstatement · cited by 1
- HomotopicalAlgebra.BifibrantObject.toHoCat_map_eq_iffstatement and proof · cited by 1