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Theorems · Theorem · category theory

HomotopicalAlgebra.FibrantObject.factorsThroughLocalization

∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C],
  (HomotopicalAlgebra.FibrantObject.homRel C).FactorsThroughLocalization
    (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.FibrantObject C))
Defined in
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy
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Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.Functor.map_comp · cited by 734Functor.map_compCategoryTheory.Functor.map_id · cited by 616Functor.map_idCategoryTheory.cancel_mono · cited by 435CategoryTheory.cancel_monoHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…CategoryTheory.MorphismProperty.Q · cited by 98MorphismProperty.QFibrantObject.factorsThroughL…CITED BYCITES

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