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Theorems · Theorem · category theory

HomotopicalAlgebra.RightHomotopyRel.factorsThroughLocalization

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C],
  HomotopicalAlgebra.RightHomotopyRel.FactorsThroughLocalization (HomotopicalAlgebra.weakEquivalences C)
Defined in
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
Cited by
1 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithWeakEquivalences
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HomotopicalAlgebra.RightHomotopyRel.iff_map_eq · cited by 0RightHomotopyRel.iff_map_…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.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Functor.map_comp · cited by 734Functor.map_compCategoryTheory.Functor.map_id · cited by 616Functor.map_idCategoryTheory.cancel_epi · cited by 380CategoryTheory.cancel_epiCategoryTheory.MorphismProperty.Q · cited by 98MorphismProperty.QHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomotopicalAlgebra.PrepathObject.P · cited by 76PrepathObject.PCategoryTheory.MorphismProperty.Localization · cited by 72MorphismProperty.Localiza…RightHomotopyRel.factorsThrou…CITED BYCITES

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