哪些类别是数量代数的变种？

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-12-02 DOI:10.1016/j.jpaa.2025.108139

Jiří Adámek

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引用次数: 0

摘要

经典的变种被Lawvere描述为具有有效同余的范畴和一个变种生成器：一个抽象有限的正则生成器，它是正则投影的（它的同函子保留正则的外胚）。我们将Mardare， Panangaden和Plotkin的数量代数的变种类似地描述为度量丰富的范畴。我们引入了次同余的概念（同余的一个度量丰富的类似物）和相应的次正则上胚，通过次同余的极限得到。定量代数的变种正是具有有效次同余的富度量范畴和一个次变量生成：一个抽象有限的次正则生成，它是次正则投影（它的同函子保留了次正则上胚）。

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Which categories are varieties of quantitative algebras?

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms).

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.