Theorems · Definition · category theory

CategoryTheory.Adjunction.fullyFaithfulLOfIsIsoUnit

{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) → [CategoryTheory.IsIso h.unit] → L.FullyFaithful

If the unit is an isomorphism, then the left adjoint is fully faithful.

Defined in

Mathlib.CategoryTheory.Adjunction.FullyFaithful

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIso