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Theorems · Theorem · category theory

HomotopicalAlgebra.FibrantObject.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 (HomotopicalAlgebra.FibrantObject.HoCat.iResolutionObj X) g =
      CategoryTheory.CategoryStruct.comp f (HomotopicalAlgebra.FibrantObject.HoCat.iResolutionObj Y)
Defined in
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy
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

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HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap · cited by 3HoCat.resolutionMapHomotopicalAlgebra.FibrantObject.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.terminal.from · cited by 77terminal.fromCategoryTheory.CommSq.lift · cited by 34CommSq.liftCategoryTheory.CommSq.fac_left · cited by 22CommSq.fac_leftCategoryTheory.Limits.terminal.comp_from · cited by 21terminal.comp_fromHomotopicalAlgebra.FibrantObject.HoCat.iResolutionObj · cited by 7HoCat.iResolutionObjHomotopicalAlgebra.FibrantObject.HoCat.resolutionObj · cited by 7HoCat.resolutionObjHoCat.exists_resolution_mapCITED BYCITES

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