关于隐式运算与平衡范畴
On implicit operations and balanced categories
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中文总结 AI 辅助
本文针对具有极值投射生成元的完备范畴，利用隐式运算刻画了平衡性及每个单态射为正则态射的更强性质，并适用于拟等式类代数。
中文摘要 AI 辅助
判断一个范畴是否为平衡的（即每个既是满态射又是单态射的态射都是同构）这一问题已被广泛研究，尤其在代数学中。对于具有极值投射生成元的完备范畴，我们以隐式运算刻画了平衡性质，以及更强的性质——每个单态射都是正则态射。这些刻画适用于例如任何拟等式类代数，可能带有真类个函数符号和无界元数，且承认自由代数。
英文摘要
The problem of determining whether a category is balanced (i.e., every morphism that is both an epimorphism and a monomorphism is an isomorphism) has been widely investigated, especially in algebra. For complete categories with an extremal projective generator, we characterise the property of being balanced, and the stronger property that every monomorphism is regular, in terms of implicit operations. These characterisations apply, for example, to any quasiequational class of algebras, possibly with a proper class of function symbols and unbounded arities, that admits free algebras.
发表机构
- Dipartimento di Matematica Federigo Enriques Università degli Studi di Milano（米兰大学费德里戈·恩里克斯数学系）
机构由 AI 辅助整理，请以论文原文为准。
