带属性的对称单一性范畴

Spencer Breiner, John S. Nolan
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引用次数: 0

摘要

在工程设计方案时,通常需要考虑与对象相关的属性,例如机器人的位置。本文的目的是将属性整合到现有的用于规划的范畴形式中,即基于对称一元范畴和弦图的范畴形式。为了实现这一点,我们定义了一个“带属性的对称一元范畴”的概念。这是一个对称的单一性范畴,其中对象配备了可检索的信息,对象和信息之间的交互由“属性结构”控制。我们在机器人上下文中讨论这些类别的示例和语义来说明我们的定义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symmetric Monoidal Categories with Attributes
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning, namely those based on symmetric monoidal categories and string diagrams. To accomplish this, we define a notion of a"symmetric monoidal category with attributes."This is a symmetric monoidal category in which objects are equipped with retrievable information and where the interactions between objects and information are governed by an"attribute structure."We discuss examples and semantics of such categories in the context of robotics to illustrate our definition.
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