Theorems · Theorem · category theory

CategoryTheory.Functor.splitEpiBiprodComparison_section_

∀ {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)] [inst_6 : F.PreservesZeroMorphisms],
  (F.splitEpiBiprodComparison X Y).section_ = F.biprodComparison' X Y

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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