Theorems · Definition · category theory

CategoryTheory.Functor.fullyFaithfulCancelRight

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            {F G : CategoryTheory.Functor C D} →
              (H : CategoryTheory.Functor D E) → [H.Full] → [H.Faithful] → (F.comp H ≅ G.comp H) → (F ≅ G)

Given a natural isomorphism between F ⋙ H and G ⋙ H for a fully faithful functor H, we can 'cancel' it to give a natural iso between F and G.

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

4 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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