Theorems · Definition · category theory

CategoryTheory.Functor.mapBiprod

{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] →
            (F : CategoryTheory.Functor C D) →
              (X Y : C) →
                [inst_4 : CategoryTheory.Limits.HasBinaryBiproduct X Y] →
                  [inst_5 : F.PreservesZeroMorphisms] →
                    [inst_6 : CategoryTheory.Limits.PreservesBinaryBiproduct X Y F] → F.obj (X ⊞ Y) ≅ F.obj X ⊞ F.obj Y

If F preserves a binary biproduct, we get a definitionally nice isomorphism F.obj (X ⊞ Y) ≅ F.obj X ⊞ F.obj Y.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

13 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproductCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesBinaryBiproduct