Theorems · Theorem · category theory

CategoryTheory.Adjunction.isLocalization_leftAdjoint

∀ {C₁ : Type u_1} {C₂ : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] {G : CategoryTheory.Functor C₁ C₂} {F : CategoryTheory.Functor C₂ C₁}
  [F.Full] [F.Faithful] (adj : G ⊣ F) (W : CategoryTheory.MorphismProperty C₁),
  W.IsInvertedBy G → W.functorCategory C₁ adj.unit → G.IsLocalization W

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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