Duality in non-abelian algebra III. Normal categories and 0-regular varieties

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• 作者：Zurab Janelidze ; Thomas Weighill
• 关键词：2010 Mathematics Subject ClassificationPrimary ; 18C99 ; Secondary ; 08A30 ; 08B05 ; 08C05 ; 18A20 ; 18A32 ; 18D30 ; 18G50
• 刊名：Algebra universalis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：77
• 期：1
• 页码：1-28
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Springer International Publishing
• ISSN：1420-8911
• 卷排序：77

文摘

Normal categories are pointed categorical counterparts of 0-regular varieties, i.e., varieties where each congruence is uniquely determined by the equivalence class of a fixed constant 0. In this paper, we give a new axiomatic approach to normal categories, which uses self-dual axioms on a functor defined using subobjects of objects in the category. We also show that a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0.