Theorems · Theorem · category theory

CategoryTheory.Functor.additive_of_preservesBinaryBiproducts

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.Preadditive C] [inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D)
  [CategoryTheory.Limits.HasBinaryBiproducts C] [inst_5 : F.PreservesZeroMorphisms]
  [CategoryTheory.Limits.PreservesBinaryBiproducts F], F.Additive

Defined in

Mathlib.CategoryTheory.Preadditive.AdditiveFunctor

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproductsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesBinaryBiproducts