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Theorems · Theorem · category theory

CategoryTheory.Limits.HasFiniteBiproducts.of_hasFiniteProducts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [CategoryTheory.Limits.HasFiniteProducts C], CategoryTheory.Limits.HasFiniteBiproducts C

A preadditive category with finite products has finite biproducts.

Defined in
Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteProducts
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CategoryTheory.Abelian.hasFiniteBiproducts · cited by 0Abelian.hasFiniteBiproduc…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteProducts · cited by 142Limits.HasFiniteProductsCategoryTheory.Limits.HasFiniteBiproducts · cited by 106Limits.HasFiniteBiproductsCategoryTheory.Limits.HasBiproduct.of_hasProduct · cited by 1HasBiproduct.of_hasProductHasFiniteBiproducts.of_hasFin…CITED BYCITES

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Cited by1

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