Practical approaches to the notions of subsets and extension sets are compared, coming from broadly set-theoretic and category-theoretic traditions of mathematics. I argue that the set-theoretic approach is the most practical for ‘looking down’ or ‘in’ at subsets and the category-theoretic approach is the most practical for ‘looking up’ or ‘out’ at extensions, and suggest some guiding principles for using these approaches without recourse to either category theory or axiomatic set theory.

中文翻译：

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向上是类别，向下是集合；淘汰类别，引进套装！

比较了来自数学的广泛集合论和范畴论传统的子集和扩展集概念的实用方法。我认为集合论方法对于“向下看”或“向内”子集最实用，而范畴论方法对于“向上查找”或“向外”扩展最实用，并提出了一些指导原则使用这些方法而不求助于范畴论或公理集合论。