Theorems · Theorem · category theory

CategoryTheory.Functor.biprodComparison_snd_assoc

∀ {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 : CategoryTheory.Limits.HasBinaryBiproduct (F.obj X) (F.obj Y)] {Z : D} (h : F.obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.biprodComparison X Y)
      (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.snd h) =
    CategoryTheory.CategoryStruct.comp (F.map CategoryTheory.Limits.biprod.snd) h

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproductCategoryTheory.Limits.HasBinaryBiproduct