论文标题
单体类别中半群对象的乘数
Multipliers of a semigroup object in a monoidal category
论文作者
论文摘要
引入了单型物类别中半群对象的乘数，这是由于普通半群的翻译船体的定义或banach代数的乘数代数的抽象而引起的，并获得了cosemigroup对象的综合材料的单型。它的固定理论版本，经典的翻译船体，可为从普通半群的子类别到单型物体提供一个函子，类似于左伴随。 Semigroup对象的抽象乘数MONOID与``具体化''同态同构的卷积半群的具体翻译船体有关。对于这种同态所涉及的半群对象，乘数构造是功能性的，具体化的同态构成了自然的表达。
The monoid of multipliers of a semigroup object in a monoidal category is introduced, arising from an abstraction of the definition of the translational hull of an ordinary semigroup or of the multiplier algebra of a Banach algebra and dually, the monoid of comultipliers of a cosemigroup object is obtained. Its set-theoretic version, the classical translational hull, is shown to provide a functor from a subcategory of ordinary semigroups to monoids, similar to a left adjoint. The abstract multiplier monoid of a semigroup object is related to the concrete translational hull of its convolution semigroup by a ``concretization'' homomorphism. For semigroup objects for which this homomorphism is onto, the multiplier construction is functorial and the concretization homomorphisms form a natural epimorphism.
