Theorems · Theorem · category theory

HomotopicalAlgebra.leftHomotopyClassToHom_mk

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {H : Type u_2} [inst_2 : CategoryTheory.Category.{v_2, u_2} H] (L : CategoryTheory.Functor C H)
  [inst_3 : L.IsLocalization (HomotopicalAlgebra.weakEquivalences C)] {X Y : C} (f : X ⟶ Y),
  HomotopicalAlgebra.leftHomotopyClassToHom L (HomotopicalAlgebra.LeftHomotopyClass.mk f) = L.map f

Defined in: Mathlib.AlgebraicTopology.ModelCategory.FundamentalLemma
Cited by: 0 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory CategoryTheory.Category CategoryTheory.Functor.IsLocalization

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapstatement · cited by 8,698
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
HomotopicalAlgebra.LeftHomotopyClass.mkstatement · cited by 14
HomotopicalAlgebra.leftHomotopyClassToHomstatement · cited by 6

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