Theorems · Theorem · category theory

CategoryTheory.Adjunction.isIso_counit_app_iff_mem_essImage

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {L : CategoryTheory.Functor C D} {R : CategoryTheory.Functor D C} (h : L ⊣ R) [L.Faithful] [L.Full] {X : D},
  CategoryTheory.IsIso (h.counit.app X) ↔ L.essImage X

Defined in

Mathlib.CategoryTheory.Adjunction.FullyFaithful

Cited by

4 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FaithfulCategoryTheory.Functor.Full