A **preadditive category** is a type of category in the field of category theory that has structures resembling abelian groups in its hom-sets. Specifically, a preadditive category satisfies the following properties: 1. **Hom-sets as Abelian Groups**: For any two objects \(A\) and \(B\) in the category, the set of morphisms \(\text{Hom}(A, B)\) forms an abelian group.
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A category is preadditive if every hom-set is an abelian group and composition is additive in each variable. Zero morphisms and differences of parallel morphisms are therefore defined. A zero object or finite biproducts need not exist; these are extra requirements in an additive category.