Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.isLocalization_isLocal

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : G ⊣ F) [F.Full] [F.Faithful],
  G.IsLocalization (CategoryTheory.ObjectProperty.isLocal fun x => x ∈ Set.range F.obj)

Defined in: Mathlib.CategoryTheory.Localization.Bousfield
Cited by: 0 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.Full CategoryTheory.Functor.Faithful

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Setstatement · cited by 53,352
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Set.rangestatement · cited by 4,705
CategoryTheory.MorphismPropertyproof · cited by 2,179
CategoryTheory.Adjunctionstatement and proof · cited by 524
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
CategoryTheory.Functor.Fullstatement and proof · cited by 341
CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
CategoryTheory.ObjectProperty.isLocalstatement · cited by 20
CategoryTheory.ObjectProperty.isLocal_eq_inverseImage_isomorphismsproof · cited by 3

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