Noun
biproduct (plural biproducts)
(category theory) A biproduct of a finite collection of objects, in a category with zero objects, is both a product and a coproduct.
An additive category is a preadditive category in which all finite biproduct exist. Source: Internet
Properties If the biproduct A ⊕ B exists for all pairs of objects A and B in the category C, then all finite biproducts exist. Source: Internet
Since our category C has a zero object, the empty biproduct exists and is isomorphic to the zero object. Source: Internet
This is because the biproduct in well known preadditive categories like Ab is the direct sum. Source: Internet