论文标题
半群的部分行动的全球化
Globalization of partial actions of semigroups
论文作者
论文摘要
我们提出了两个半群在集合中的部分作用的全球化的普遍构造，满足了莫里塔半群理论中出现的某些条件。其中一种结构是基于与半群的部分半群法的张量产物，并概括了由于Megrelishvili和Schröder而导致的全球化构造Monoids的强烈部分作用。它在适当的全球化餐饮上产生了初始对象。另一个构造涉及$ {\ mathrm {hom}} $ - 即使在单体设置中也是新颖的。它在适当的全球化类别中产生终端对象。尽管在组中，这两个构建体的结果是同构的，但在单体情况下它们可能会大不相同。
We propose two universal constructions of globalization of a partial action of a semigroup on a set, satisfying certain conditions which arise in Morita theory of semigroups. One of the constructions is based on the tensor product of a partial semigroup act with the semigroup and generalizes the globalization construction of strong partial actions of monoids due to Megrelishvili and Schröder. It produces the initial object in an appropriate caterory of globalizations of a given partial action. The other construction involves ${\mathrm{Hom}}$-sets and is novel even in the monoid setting. It produces the terminal object in an appropriate category of globalizations. While in the group case the results of the two constructions are isomorphic, they can be far different in the monoid case.
