Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.isLocal_eq_inverseImage_isomorphisms

∀ {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],
  (CategoryTheory.ObjectProperty.isLocal fun x => x ∈ Set.range F.obj) =
    (CategoryTheory.MorphismProperty.isomorphisms C).inverseImage G

Defined in

Mathlib.CategoryTheory.Localization.Bousfield

Cited by

3 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful