Convexity, Duality and Effects
Convexity, Duality and Effects
复制标题
凸性、对偶性和效应
DOI：
10.1007/978-3-642-15240-5_1
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. Jacobs
中科院分区：
文献类型：
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作者：
B. Jacobs
本文描述了量子逻辑和概率中相关的数学结构之间的一些基本关系，即凸集，效应代数和一类新的函子，我们称之为“凸函子”;它们包括通常称为概率分布函子的东西。这些关系表现为三个方面。这三个中的两个是凸集的“对偶”映射，一次是布尔真值{0，1}作为对偶对象，另一次是概率值[0，1]。第三个附加是在效果代数和凸函子之间。
This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call ‘convex functors’; they include what are usually called probability distribution functors. These relationships take the form of three adjunctions. Two of these three are ‘dual’ adjunctions for convex sets, one time with the Boolean truth values {0,1} as dualising object, and one time with the probablity values [0,1]. The third adjunction is between effect algebras and convex functors.