巴拿赫空间直接积分的范畴框架
A Categorical Framework for the Direct Integration of Banach Spaces
首次发表
浏览论文内容
中文总结 AI 辅助
该研究构建了抽象巴拿赫丛的拟阿贝尔范畴作为范畴框架，将直接积分定义为输入抽象巴拿赫丛对象、输出巴拿赫空间的函子，进而定义了层的直接积分概念。
中文摘要 AI 辅助
我们构建了一个范畴框架，可将直接积分视为函子，以某类抽象巴拿赫丛范畴中的对象为输入，输出一个巴拿赫空间。为此，我们构建了抽象巴拿赫丛的拟阿贝尔范畴，并证明了该范畴及其对象的若干基础理论结果。由此，我们得以定义层的直接积分概念。
英文摘要
We construct a categorical framework in which we can view the direct integral as a functor taking as input objects in a certain category of Abstract Banach bundles and outputting a Banach space. We do this by constructing a quasi-abelian category of abstract Banach bundles, and we prove certain foundational and theoretical results about this category and its objects. As a consequence, we are able to define a notion of direct integral of sheaves.
