Theorems · Definition · category theory

CategoryTheory.Functor.mapBiproduct

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            {J : Type w₁} →
              (F : CategoryTheory.Functor C D) →
                (f : J → C) →
                  [inst_4 : CategoryTheory.Limits.HasBiproduct f] →
                    [inst_5 : F.PreservesZeroMorphisms] →
                      [inst_6 : CategoryTheory.Limits.PreservesBiproduct f F] → F.obj (⨁ f) ≅ ⨁ F.obj ∘ f

If F preserves a biproduct, we get a definitionally nice isomorphism F.obj (⨁ f) ≅ ⨁ (F.obj ∘ f).

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

5 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBiproductCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesBiproduct