Theorems · Definition · category theory

CategoryTheory.Limits.isBinaryBilimitOfPreserves

{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] →
            {X Y : C} →
              (F : CategoryTheory.Functor C D) →
                [inst_4 : F.PreservesZeroMorphisms] →
                  [CategoryTheory.Limits.PreservesBinaryBiproduct X Y F] →
                    {b : CategoryTheory.Limits.BinaryBicone X Y} → b.IsBilimit → (F.mapBinaryBicone b).IsBilimit

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

6 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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