Biproducts always exist within the class of abelian agencies. In that class, the biproduct of several gadgets is in reality their direct sum. The nullary biproduct is the 'group. Biproducts exist in several other classes with direct sums, including the class of vector
spaces over a given subject. But biproducts do not exist inside the class of all groups; indeed, this class isn't always even preadditive. F a nullary biproduct exists and all binary biproducts A1 ⊕ A2 exist, then all biproducts in any way should also exist. Biproducts in preadditive categories are always each products and coproducts inside the regular class-theoretic feel; this is the foundation of the time period "biproduct". In unique, a nullary biproduct is usually a 0 object. Conversely, any finitary product or coproduct in a preadditive class should be a biproduct. An additive class is a preadditive category wherein each biproduct exists. In specific, biproducts always exist in abelian categories.
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