图解的负信息
Diagrammatic Negative Information
AI总结：
本文提出利用函子串图这一新颖图解方法，在范畴论中自然地表示负信息，解决了传统 nategories 放弃核心范畴构造的问题，并为三角不等式和 $\mathbf{DP/Feas_{Bool}}$ 等负信息复合提供了系统化的图解工具。
摘要：
复杂系统中的信息流动可以通过范畴论来轻松理解。然而，负信息（例如，什么是不可能的）并没有一个直接且明显的范畴表示。使用非传统复合对 nategories 进行形式化解决了这个问题，并允许考虑对范畴施加的限制。然而，传统的 nategories 放弃了核心的范畴构造，并依赖于大量的数学发展。这在正信息和负信息复合的考量之间造成了鸿沟。在这项工作中，我们展示了负信息可以以自然的范畴方式被考虑。这得益于函子串图（functor string diagrams），这是一种新颖且灵活的图解方法，能够直观地展示表达式中 hom-functors 和自然变换的运作。这一见解揭示了如何在不依赖 enrichment 的情况下，考虑负信息与基础范畴构造的复合。我们提出了不仅考虑 nategories，而且更广泛地考虑预序的图解手段。本文引入了考虑三角不等式的图解方法，并共同设计了 $\mathbf{DP/Feas_{Bool}}$，展示了负信息复合的重要案例如何以范畴和图解的方式被处理。特别地，我们开发了系统工具来严格考虑对系统施加的限制，推进了我们的数学理解，并提出了直观的图表，以促进其在各种应用中的广泛采用和使用。
英文摘要：
The flow of information through a complex system can be readily understood with category theory. However, negative information (e.g., what is not possible) does not have an immediately evident categorical representation. The formalization of nategories using unconventional composition addresses this issue, and lets imposed limitations on categories be considered. However, traditional nategories abandon core categorical constructs and rely on extensive mathematical development. This creates a divide between the consideration of positive and negative information composition. In this work, we show that negative information can be considered in a natural categorical manner. This is aided by functor string diagrams, a novel flexible diagrammatic approach that can intuitively show the operation of hom-functors and natural transformations in expressions. This insight reveals how to consider the composition of negative information with foundational categorical constructs without relying on enrichment. We present diagrammatic means to consider not only nategories, but preorders more broadly. This paper introduces diagrammatic methods for the consideration of triangle inequalities and co-designs $\mathbf{DP/Feas_{Bool}}$, showing how important cases of negative information composition can be categorically and diagrammatically approached. In particular, we develop systematic tools to rigorously consider imposed limitations on systems, advancing our mathematical understanding, and present intuitive diagrams which motivate widespread adoption and usage for various applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
