如何将闭包和内部操作扩展到更多模块

Pub Date : 2023-12-01 DOI:10.1017/nmj.2023.36

NEIL EPSTEIN, REBECCA R. G., JANET VASSILEV

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引用次数: 1

摘要

有几种方法可以将闭包或内部操作转换为具有特定期望属性的不同操作。在本文中，我们公化了三种方法来做到这一点，从文献中吸取不同的例子，包括紧闭包，基本完全闭包和各种版本的积分闭包。在这样做的过程中，我们探索了几个这样的理想性质，包括遗传、剩余和共同的，并看到它们如何与其他性质(如有限性质)相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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HOW TO EXTEND CLOSURE AND INTERIOR OPERATIONS TO MORE MODULES

There are several ways to convert a closure or interior operation to a different operation that has particular desirable properties. In this paper, we axiomatize three ways to do so, drawing on disparate examples from the literature, including tight closure, basically full closure, and various versions of integral closure. In doing so, we explore several such desirable properties, including hereditary, residual, and cofunctorial, and see how they interact with other properties such as the finitistic property.

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