Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.isColocal_iff_isIso_map

∀ {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) [G.Full] [G.Faithful] {X Y : C} (f : X ⟶ Y),
  CategoryTheory.ObjectProperty.isColocal (fun x => x ∈ Set.range G.obj) f ↔ CategoryTheory.IsIso (F.map f)

Defined in

Mathlib.CategoryTheory.Localization.Bousfield

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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