发表机构
University of Gothenburg; Università degli Studi di Milano（哥德堡大学; 米兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对局部有限呈现范畴构造Beth伴随，证明其唯一性，给出计算与句法表示方法，确立性质转移条件，为范畴论相关研究提供理论支撑。
AI 中文摘要
对于范畴而言，平衡（即每个同时为满态和单态的态射都是同构）可视为一种强驯服性质，例如在代数和逻辑中发挥重要作用。我们研究将平衡伴随范畴（称为Beth伴随）关联到局部有限呈现范畴（等价于有限本质代数理论的模型范畴）的问题。我们证明，若Beth伴随存在，则其唯一且可通过饱和对象描述。在一些额外假设下，我们证明Beth伴随可作为正交类计算，并可通过Gabriel-Ulmer对偶性获得句法表示。最后，我们建立性质转移的条件，例如确保若原范畴等价于一个（拟）簇，其Beth伴随也等价于该类。
英文摘要
For categories, being balanced (meaning that every arrow that is both epic and monic is an isomorphism) can be regarded as a strong tameness property which plays an important role, for example, in algebra and logic. We study the problem of associating a balanced companion category, called \emph{Beth companion}, to a locally finitely presentable category (equivalently, the category of models of a finitary essentially algebraic theory). We show that, if it exists, the Beth companion is unique and can be described in terms of \emph{saturated} objects. Under some additional assumptions, we prove that Beth companions can be computed as orthogonality classes, and admit a syntactic presentation via Gabriel--Ulmer duality. Finally, we establish conditions for the transfer of properties, ensuring, for instance, that if the original category is equivalent to a (quasi)variety, its Beth companion is too.
Commentsv1: 31 pages
