Theorems · Definition · category theory

CategoryTheory.Functor.preimageIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) → {X Y : C} → [F.Full] → [F.Faithful] → (F.obj X ≅ F.obj Y) → (X ≅ Y)

If F : C ⥤ D is fully faithful, every isomorphism F.obj X ≅ F.obj Y has a preimage.

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

14 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Classical.choice

Assumes

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