半阿贝尔范畴中的三元半直积
Ternary semi-direct products in semi-abelian categories
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中文总结 AI 辅助
本文在半阿贝尔范畴中定义并研究了三元半直积，证明其由满足相容条件的作用和等变态射决定，并探讨了在特定范畴中的简化及与群、李代数版本的关联。
中文摘要 AI 辅助
我们研究了半阿贝尔范畴中三元半直积的构造，遵循Carrasco和Cegarra先前为群和李代数引入的高阶半直积定义。我们证明这些对象由作用和在环境范畴中满足特定相容条件的等变态射决定，并且半直积作用是该构造的特例。我们还展示了在代数相干或局部代数笛卡尔闭范畴中，其结构如何进一步简化。我们还给出了具体范畴中三元半直积结构的具体描述，以及我们对必要结构的范畴论解释如何与Carrasco和Cegarra给出的群和李理论版本相关联。
英文摘要
We study the construction of ternary semi-direct products in semi-abelian categories, following a definition of higher semi-direct product previously introduced by Carrasco and Cegarra for groups and Lie algebras. We show that these objects are determined by actions and equivariant morphisms satisfying a certain compatibility condition in the ambient category, and that actions by semi-direct products are a special case of this construction. We also show how their structure can be further simplified in algebraically coherent or locally algebraically cartesian closed categories. We also give a concrete description of the structure of ternary semi-direct products in concrete categories, and how our categorical interpretation of the necessary structure relates to the group and Lie-theoretic versions given by Carrasco and Cegarra.
发表机构
- Université catholique de Louvain（天主教鲁汶大学）
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