Theorems · Theorem · category theory

CategoryTheory.Functor.splitEpiBiproductComparison_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] {J : Type w₁}
  (F : CategoryTheory.Functor C D) (f : J → C) [inst_4 : CategoryTheory.Limits.HasBiproduct f]
  [inst_5 : CategoryTheory.Limits.HasBiproduct (F.obj ∘ f)] [inst_6 : F.PreservesZeroMorphisms],
  (F.splitEpiBiproductComparison f).section_ = F.biproductComparison' f

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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