Theorems · Definition · category theory

CategoryTheory.equivEssImageOfReflective

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {i : CategoryTheory.Functor D C} → [CategoryTheory.Reflective i] → D ≌ i.EssImageSubcategory

If i : D ⥤ C is reflective, the inverse functor of i ≌ F.essImage can be explicitly defined by the reflector.

Defined in

Mathlib.CategoryTheory.Adjunction.Reflective

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Reflective