Varieties of quantitative algebras as categories
arxiv(2024)
摘要
Varieties of quantitative algebras of Mardare, Panangaden and Plotkin are characterized as certain categories enriched over metric spaces. We introduce the concept of a procongruence (a metric-enriched analogue of a congruence) and the corresponding proexact categories. Varieties of quantitative algebras are precisely the metric-enriched proexact categories with a provarietal generator. This means an abstractly finite, strong generator whose hom-functor preserves proregular epimorphisms.
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