论文标题
类别理论的工作方式：元素，二元性和普遍构造的元素和区别分析
How Category Theory Works: The Elements & Distinctions Analysis of the Morphisms, Duality, and Universal Constructions in Sets
论文作者
论文摘要
本文的目的是表明元素和区别的双重概念是在集合中解开和分析形态，双重性和通用构造所需的基本分析概念，集合和功能的类别。该分析直接扩展到其他具体类别（组，环，矢量空间等），其中设置对象具有某种类型的结构，并且形态是保留该结构的函数。然后，对于抽象类别理论，可以以纯箭头理论方式将基于元素和区别的定义抽象。简而言之，元素和区分的语言是书面类别的概念语言，抽象类别理论给出了这些定义的抽象箭头版本。
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions.
