Theorems · Theorem · category theory

CategoryTheory.Functor.eq_of_iso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F₁ F₂ : CategoryTheory.Functor D C} [Quiver.IsThin C], CategoryTheory.Skeletal C → ∀ (hF : F₁ ≅ F₂), F₁ = F₂

If C is thin and skeletal, then any naturally isomorphic functors to C are equal.

Defined in

Mathlib.CategoryTheory.Skeletal

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryQuiver.IsThin