关于我最喜欢的在范畴论中画缺失图的约定
On my favorite conventions for drawing the missing diagrams in Category Theory
摘要：
我曾经相信，我的公约绘制图表的分类语句可以写下来在一页或更少，唯一棘手的部分是技术重建对象“从他们的名字”。但后来我发现事实并非如此。这是一个试图解释，动机和例子，所有的约定背后的某个图表，所谓的“基本例子”的文字。一旦理解了这些约定，图就成为与米田引理相关的某个引理的“骨架”，在这个意义上，这个引理的陈述和证明都可以从图中重建出来。最后一节讨论了一些简单的方法来扩展约定;我们看到如何在图中表示（“真实”）Yoneda引理及其推论，如何定义逗号范畴，以及如何形式化“儿童几何态射”的图。CT中的人们通常只在他们的图表跨越数学相关性的阈值时分享他们可视化事物的方式-这通常发生在他们用图表证明新定理时，或者当他们可以证明他们的图表可以将曾经巨大的计算转化为更容易可视化的东西时。我在这里介绍的图解语言低于这一门槛，因此它是一种“私人的”图解语言，我将其公开，是为了与其他人建立对话，这些人也创造了自己的私人图解语言。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
