某些半群子范畴中的张量积

半群范畴S中张量积首先在中引入。T∈ob S称为A,B∈ob S的张量积(记为AB),如果存在双同态t:A×B→T(相当于中线性平衡映射),且对于任意双同态s:A×B→C∈ob S总存在唯一的同态μ:T→C,使s-ut。确认了张量积的存在唯一。等引入交换半群、半格等子范畴中的张量积,其定义与上述基本相同,仅将S改为该子范畴,此外该划了一些半群类的张量积。本文在§1从任意半群簇V中张量积与其在S中

On the Tensor Products in Som e Subcategories of Semigroups

In this paper the existence and uniqueness of tensor product in any semigroup variety are proved, and the relation between the tensor products in semigroup variety and in semigroup category is charaterized. Next, we consider the existence and uniqueness of tensor product in cancellation commutative semigr-oup subcategory, this tensor product is a subsemigroup of tensor product of two quotient groups in abelian group category.