限制范畴中的覆盖与更新
Override and Update in Restriction Categories
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中文总结 AI 辅助
本文从限制范畴视角研究部分函数的覆盖与更新算子，定义覆盖限制范畴，证明相关结果并给出例子，表明每个经典限制范畴都是覆盖限制范畴。
中文摘要 AI 辅助
我们从限制范畴的视角研究部分函数上的覆盖（override）与更新（update）算子，提出覆盖限制范畴的定义，该范畴中存在所讨论的两种算子。我们证明了一系列关于这些算子及其与周围限制范畴结构关系的结果，并将其与现有关于覆盖和更新算子的文献相关联。我们给出覆盖限制范畴的多个例子，特别证明每个经典限制范畴都是覆盖限制范畴。
英文摘要
We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which both of the operators in question exist. We prove a number of results concerning these operators and their relationship to the structure of the ambient restriction category, as well as relating them to the existing literature on the override and update operators. We provide various examples of override restriction categories and in particular show that every classical restriction category is an override restriction category.
发表机构
- Macquarie University（麦考瑞大学）
- University of Tartu（塔尔图大学）
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