标题： 目录：类别系统理论中层次组织的方便且表现良好的形式化方法 显示英文标题

标题： Directories: A Convenient and Well-Behaved Formalism for Hierarchical Organization in Categorical Systems Theory

摘要： 本文介绍了一种本质上严格的范畴表示方法，该方法受到文件系统和目录的启发，涵盖了积范畴、余积范畴或对称单调乘积范畴。与使用嵌套二元组来组合对象或态射不同，这种表示方法使用命名元组。具体来说，我们发展了2-单子，其严格2-代数分别是积范畴、余积范畴或对称单调范畴，类似于经典的Fam构造，但这里索引集的元素是形如$\mathtt{cart.motor.momentum}$的周期分隔标识符。我们对目录的发展也旨在阐述多项式单子的某些方面，并附有Haskell代码，展示了如何实现这些数学思想。 显示英文摘要

摘要： This paper introduces an inherently strict presentation of categories with products, coproducts, or symmetric monoidal products that is inspired by file systems and directories. Rather than using nested binary tuples to combine objects or morphisms, the presentation uses named tuples. Specifically, we develop 2-monads whose strict 2-algebras are product categories, coproduct categories, or symmetric monoidal categories, in a similar vein to the classical Fam construction, but where the elements of the indexing set are period-separated identifiers like $\mathtt{cart.motor.momentum}$. Our development of directories is also intended to serve the secondary purpose of expositing certain aspects of polynomial monads, and is accompanied by Haskell code that shows how the mathematical ideas can be implemented.