Theorems · Theorem · category theory

HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  [inst_2 : HomotopicalAlgebra.IsCofibrant X] [inst_3 : HomotopicalAlgebra.IsCofibrant Y]
  [inst_4 : HomotopicalAlgebra.IsFibrant X] [inst_5 : HomotopicalAlgebra.IsFibrant Y] (f : X ⟶ Y),
  HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight (HomotopicalAlgebra.RightHomotopyClass.mk f) =
    HomotopicalAlgebra.BifibrantObject.toHoCat.map (HomotopicalAlgebra.BifibrantObject.homMk f)

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by: 0 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsFibrant HomotopicalAlgebra.IsFibrant

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DFunLike.coestatement · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functor.mapstatement · cited by 8,698
Equivstatement · cited by 8,337
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
HomotopicalAlgebra.BifibrantObjectstatement · cited by 38
HomotopicalAlgebra.bifibrantObjectsstatement · cited by 37
HomotopicalAlgebra.BifibrantObject.homRelstatement · cited by 22

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