A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as ‘machines’ with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include continuous and discrete dynamical systems (e.g. Moore machines). Additionally, morphisms between the different types of systems allow their translation in a common framework. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems, possibly of different types, as well as establish conditions that ensure totality and determinism compositionally. The fundamental categorical tools used here include lax monoidal functors, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time.

中文翻译：

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动力系统和滑轮

提出了一个广义的建模和分析系统的分类框架。这些系统应该被认为是具有输入和输出的“机器”，携带通过某种时间概念发生的某种信号。特殊情况包括连续和离散动力系统（例如摩尔机）。此外，不同类型系统之间的态射允许它们在公共框架中进行转换。一个中心目标是了解由组件子系统（可能是不同类型）的任意互连产生的系统，并建立条件以确保整体性和确定性。这里使用的基本分类工具包括松散幺半群函子，它提供了一种组合语言，以及层理论，它灵活地捕捉了时间的关键概念。