论文标题
尖的半副型
Pointed semibiproducts of monoids
论文作者
论文摘要
此处引入了单粒细胞的半副型，作为对双植物（Abelian群体）的常见概括，并以（组的）（组）探索一类巨大的单粒子扩展。更一般而言，在任何具体类别中都存在抽象的半脂肪，而在该集合中，MAP添加是有意义的，从而重新解释了Mac Lane的相对双质源。在尖锐的情况下，它们产生了一种特殊的扩展类别，称为半脱头扩展。并非所有的单粒扩展都是半iProduct扩展，但所有组扩展均为。在尖头的半肌动物类别与尖头单体动作系统的类别之间建立了分类等效性，这是一种从等效性出现的新的动作类别。与经典扩展理论的主要区别在于，即使截面映射可能并未成为同态，即使截面映射可能并不是分裂扩展的方式，也以与拆分扩展相同的方式处理。提供了所有14个2元素单型单粒子的列表。
Semibiproducts of monoids are introduced here as a common generalization to biproducts (of abelian groups) and to semidirect products (of groups) for exploring a wide class of monoid extensions. More generally, abstract semibiproducts exist in any concrete category over sets in which map addition is meaningful thus reinterpreting Mac Lane's relative biproducts. In the pointed case they give rise to a special class of extensions called semibiproduct extensions. Not all monoid extensions are semibiproduct extensions but all group extensions are. A categorical equivalence is established between the category of pointed semibiproducts of monoids and the category of pointed monoid action systems, a new category of actions that emerges from the equivalence. The main difference to classical extension theory is that semibiproduct extensions are treated in the same way as split extensions, even though the section map may fail to be a homomorphism. A list with all the 14 semibiproduct extensions of 2-element monoids is provided.
