Theorems · Theorem · category theory

HomotopicalAlgebra.CofibrantObject.homMk_homMk

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] {X Y Z : C} [inst_3 : HomotopicalAlgebra.IsCofibrant X]
  [inst_4 : HomotopicalAlgebra.IsCofibrant Y] [inst_5 : HomotopicalAlgebra.IsCofibrant Z] (f : X ⟶ Y) (g : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomotopicalAlgebra.CofibrantObject.homMk f)
      (HomotopicalAlgebra.CofibrantObject.homMk g) =
    HomotopicalAlgebra.CofibrantObject.homMk (CategoryTheory.CategoryStruct.comp f g)

Defined in: Mathlib.AlgebraicTopology.ModelCategory.Bifibrant
Cited by: 1 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations CategoryTheory.Limits.HasInitial HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsCofibrant

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Cites10

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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.CofibrantObjectstatement · cited by 35
HomotopicalAlgebra.cofibrantObjectsstatement · cited by 34
HomotopicalAlgebra.CofibrantObject.mkstatement · cited by 16
HomotopicalAlgebra.CofibrantObject.homMkstatement · cited by 13

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.CofibrantObject.homMk_homMk_assocproof · cited by 0