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

被引：0
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作者：
Zurab Janelidze
Thomas Weighill
机构：
[1] Stellenbosch University,Mathematics Division, Department of Mathematical Sciences
[2] University of Tennessee,Department of Mathematics
来源：
Algebra universalis | 2017年 / 77卷
关键词：
Primary: 18C99; Secondary: 08A30; 08B05; 08C05; 18A20; 18A32; 18D30; 18G50; abelian category; axiomatic duality; exact form; Grothendieck fibration; homological category; form of subobjects; ideal-determined variety; normal category; 0-permutable variety; protomodular category; 0-regular variety; semi-abelian category; subobject fibration; subtractive category; subtractive variety; universalizer; variety with ideals;
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学科分类号：
摘要：
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.
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页码：1 / 28
页数：27
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