Theorems · Theorem · category theory

CategoryTheory.Adjunction.isIso_map_unit_of_isLeftAdjoint_comp

∀ {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) {E : Type u_1}
  [inst_2 : CategoryTheory.Category.{v_1, u_1} E] {T : CategoryTheory.Functor C E} {S : CategoryTheory.Functor E D}
  {X : C} (adj2 : T ⊣ S.comp R) [R.Faithful] [R.Full], CategoryTheory.IsIso (T.map (h.unit.app X))

Defined in

Mathlib.CategoryTheory.Adjunction.FullyFaithful

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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