Theorems · Inductive type · category theory

CategoryTheory.Limits.PreservesBinaryBiproduct

{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] →
            C → C → (F : CategoryTheory.Functor C D) → [F.PreservesZeroMorphisms] → Prop

A functor F preserves binary biproducts of X and Y if F maps every bilimit bicone over X and Y to a bilimit bicone over F.obj X and F.obj Y.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

15 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms