论文标题
离散时间反馈的梳子图
Comb Diagrams for Discrete-Time Feedback
论文作者
论文摘要
应用类别理论中许多有用的双向结构的数据（光学，学习者，游戏，量子梳）可以用包含“孔”或“不完整部分”的图表表示，有时称为梳子图。我们使用由coend产生的dinaturaty等效关系来对这些不完整部分的这些电路表示形式化。我们的主要思想是扩展此正式描述，以允许自然数字索引的无限电路。我们展示了如何在任意对称单体类别上的无限梳再次形成一种对称单体类别，其中可以考虑延迟和反馈的概念。这里提出的结构仍然是初步工作。
The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing "holes" or "incomplete parts", sometimes known as comb diagrams. We give a possible formalization of what these circuits with incomplete parts represent in terms of symmetric monoidal categories, using the dinaturality equivalence relations arising from a coend. Our main idea is to extend this formal description to allow for infinite circuits with holes indexed by the natural numbers. We show how infinite combs over an arbitrary symmetric monoidal category form again a symmetric monoidal category where notions of delay and feedback can be considered. The constructions presented here are still preliminary work.
