Theorems · Definition · category theory

HomotopicalAlgebra.CofibrantObject.toHoCatLocalizerMorphism

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] →
      CategoryTheory.LocalizerMorphism (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.CofibrantObject C))
        (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.CofibrantObject.HoCat C))

The functor CofibrantObject C ⥤ HoCat C, considered as a localizer morphism.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy
Cited by: 0 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homproof · cited by 32,603
CategoryTheory.LocalizerMorphismstatement · cited by 161
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
HomotopicalAlgebra.CofibrantObjectstatement and proof · cited by 35
HomotopicalAlgebra.cofibrantObjectsstatement · cited by 34
HomotopicalAlgebra.CofibrantObject.homRelstatement · cited by 20
HomotopicalAlgebra.CofibrantObject.HoCatstatement · cited by 17
HomotopicalAlgebra.CofibrantObject.toHoCatproof · cited by 14

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