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Theorems · Theorem · category theory

HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolution_map

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  (f : X ⟶ Y),
  ∃ g,
    CategoryTheory.CategoryStruct.comp g (HomotopicalAlgebra.CofibrantObject.HoCat.pResolutionObj Y) =
      CategoryTheory.CategoryStruct.comp (HomotopicalAlgebra.CofibrantObject.HoCat.pResolutionObj X) f
Defined in
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap · cited by 3HoCat.resolutionMapHomotopicalAlgebra.CofibrantObject.HoCat.resolutionMap_fac · cited by 2HoCat.resolutionMap_facCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CommSq · cited by 158CategoryTheory.CommSqHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…CategoryTheory.Limits.initial.to · cited by 63initial.toCategoryTheory.CommSq.lift · cited by 34CommSq.liftCategoryTheory.CommSq.fac_right · cited by 19CommSq.fac_rightCategoryTheory.Limits.initial.to_comp · cited by 11initial.to_compHomotopicalAlgebra.CofibrantObject.HoCat.pResolutionObj · cited by 6HoCat.pResolutionObjHomotopicalAlgebra.CofibrantObject.HoCat.resolutionObj · cited by 6HoCat.resolutionObjHoCat.exists_resolution_mapCITED BYCITES

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Cited by2

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