We prove that the profinite completion construction is a covariant functor from the category of (universal) algebras of a given type into the category of the corresponding Stone algebras. A Grothendieck problem for finitely presented MV-algebras is also formulated and solved. Finally, we characterize finitely presented MV-algebras for which profinite completions and MacNeille completions coincide.

中文翻译：

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有限呈现的 MV 代数的有限完成和 MacNeille 完成

我们证明了有限补全构造是从给定类型的（通用）代数范畴到对应的斯通代数范畴的协变函子。有限呈现的 MV 代数的格洛腾迪克问题也被制定和解决。最后，我们描述了有限完成和 MacNeille 完成一致的有限呈现 MV 代数。