Theorems · Theorem · category theory

HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {X Y : HomotopicalAlgebra.CofibrantObject C} {f g : X ⟶ Y},
  HomotopicalAlgebra.CofibrantObject.homRel C f g →
    HomotopicalAlgebra.CofibrantObject.toHoCat.map f = HomotopicalAlgebra.CofibrantObject.toHoCat.map g

Defined in: Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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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.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functor.mapstatement · cited by 8,698
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.CofibrantObjectstatement and proof · cited by 35
HomotopicalAlgebra.cofibrantObjectsstatement · cited by 34
HomotopicalAlgebra.CofibrantObject.homRelstatement and proof · cited by 20
HomotopicalAlgebra.CofibrantObject.HoCatstatement · cited by 17
CategoryTheory.Quotient.soundproof · cited by 16
HomotopicalAlgebra.CofibrantObject.toHoCatstatement · cited by 14

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.CofibrantObject.HoCat.resolutionObj_hom_extproof · cited by 0