论文标题
在我最喜欢的惯例上，用于绘制类别理论中缺少图的图表
On my favorite conventions for drawing the missing diagrams in Category Theory
论文作者
论文摘要
我曾经相信，我的分类语句绘制图表的惯例可以写在一页或更少的时间内，唯一的棘手部分是重建对象“来自其名称”的技术...但是后来我发现并非如此。 这是一种尝试用动机和示例来解释特定图背后的所有惯例，即文本中称为“基本示例”。一旦理解了惯例，就可以从图中重建了陈述和该引理的陈述和证据，这将成为与Yoneda引理有关的某些引理的“骨架”。最后一节讨论了一些扩展惯例的简单方法；我们看到了如何在图中表达（“真实”）Yoneda引理及其推论，如何定义逗号类别以及如何形式化“儿童的几何形态”图。 CT中的人们通常只分享他们的图表的方式时，当他们的图表越过数学相关性的某个门槛时 - 通常会发生在用图表证明新定理时，或者当他们可以证明其图可以将其图表转化为较大的事物的计算中，这些内容易于可视化。我在这里提出的图形语言在于该阈值以下 - 因此，这是一种“私人”的图解语言，我正在公开以与其他人建立自己的私人图形语言的其他人进行对话。
I used to believe that my conventions for drawing diagrams for categorical statements could be written down in one page or less, and that the only tricky part was the technique for reconstructing objects "from their names"... but then I found out that this is not so. This is an attempt to explain, with motivations and examples, all the conventions behind a certain diagram, called the "Basic Example" in the text. Once the conventions are understood that diagram becomes a "skeleton" for a certain lemma related to the Yoneda Lemma, in the sense that both the statement and the proof of that lemma can be reconstructed from the diagram. The last sections discuss some simple ways to extend the conventions; we see how to express in diagrams the ("real") Yoneda Lemma and a corollary of it, how to define comma categories, and how to formalize the diagram for "geometric morphism for children". People in CT usually only share their ways of visualizing things when their diagrams cross some threshold of of mathematical relevance - and this usually happens when they prove new theorems with their diagrams, or when they can show that their diagrams can translate calculations that used to be huge into things that are much easier to visualize. The diagrammatic language that I present here lies below that threshold - and so it is a "private" diagrammatic language, that I am making public as an attempt to establish a dialogue with other people who have also created their own private diagrammatic languages.
