Theorems · Definition · category theory

CategoryTheory.Mat_.ext

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {D : Type u₁} →
        [inst_2 : CategoryTheory.Category.{v₁, u₁} D] →
          [inst_3 : CategoryTheory.Preadditive D] →
            [CategoryTheory.Limits.HasFiniteBiproducts D] →
              {F G : CategoryTheory.Functor (CategoryTheory.Mat_ C) D} →
                [F.Additive] →
                  [G.Additive] →
                    ((CategoryTheory.Mat_.embedding C).comp F ≅ (CategoryTheory.Mat_.embedding C).comp G) → (F ≅ G)

Two additive functors Mat_ C ⥤ D are naturally isomorphic if their precompositions with embedding C are naturally isomorphic as functors C ⥤ D.

Defined in

Mathlib.CategoryTheory.Preadditive.Mat

Cited by

0 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteBiproductsCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Additive