Theorems · Definition · category theory

CategoryTheory.Functor.sumIsoExt

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {C : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {F G : CategoryTheory.Functor (A ⊕ B) C} →
              ((CategoryTheory.Sum.inl_ A B).comp F ≅ (CategoryTheory.Sum.inl_ A B).comp G) →
                ((CategoryTheory.Sum.inr_ A B).comp F ≅ (CategoryTheory.Sum.inr_ A B).comp G) → (F ≅ G)

A functor out of a sum is uniquely characterized by its precompositions with inl_ and inr_.

Defined in

Mathlib.CategoryTheory.Sums.Basic

Cited by

4 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category