Pre-semihyperadditive Categories

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects A and B , the class of all morphisms from A to B denoted by Mor ( A, B ), admits an algebraic hyperstructures, such as semihypergroup or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semihyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories.