This paper establishes the tensor products in medial semigroup category and proves their existence and uniqueness. Furthermore, it sets up the relation between the maximal separative semigroup images and the tensor prodects of exponential semigroups.%建立平均可分半群范畴中的张量积,证明其存在与唯一性,同时,建立平均半群的极大可分半群象与张量积之间的关系.
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