Theorems · Theorem · category theory

CategoryTheory.Limits.preservesBinaryBiproduct_of_preservesBinaryProduct

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {D : Type u'}
  [inst_2 : CategoryTheory.Category.{v', u'} D] [inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D)
  [inst_4 : F.PreservesZeroMorphisms] {X Y : C}
  [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair X Y) F],
  CategoryTheory.Limits.PreservesBinaryBiproduct X Y F

A functor between preadditive categories that preserves (zero morphisms and) binary products preserves binary biproducts.

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesLimit