Theorems · Definition · category theory

CategoryTheory.Limits.biproduct.matrixEquiv

{J : Type} →
  [inst : Finite J] →
    {K : Type} →
      [inst_1 : Finite K] →
        {C : Type u} →
          [inst_2 : CategoryTheory.Category.{v, u} C] →
            [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C] →
              [inst_4 : CategoryTheory.Limits.HasFiniteBiproducts C] →
                {f : J → C} → {g : K → C} → (⨁ f ⟶ ⨁ g) ≃ ((j : J) → (k : K) → f j ⟶ g k)

Morphisms between direct sums are matrices.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

2 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteFiniteCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasFiniteBiproducts