论文标题
类别理论中的一些图表追逐和图解证明的注释
Some notes on diagram chasing and diagrammatic proofs in category theory
论文作者
论文摘要
示意图追逐是类别理论和同源代数中使用的习惯证明方法。它涉及一种元素理论方法，以表明某些属性适用于通勤图。在第一次处理Abelian类别时，人们将使用图形方法进行工作，而不必依赖元素的概念。但是，不断操纵各个图的通用性能可能很麻烦。也就是说，我们认为在两个观点之间进行对比以激发类别理论领域仍然很重要。我们将范围集中在短五引理上，这是较基本图的引理之一，并对相关主题进行了快速阐述。此外，我们使用回调的通用属性给出了简短的五个引理的原始证明。
Diagram chasing is a customary proof method used in category theory and homological algebra. It involves an element-theoretic approach to show that certain properties hold for a commutative diagram. When dealing with abelian categories for the first time, one would work using a diagrammatic approach without relying on the notion of elements. However, constantly manipulating universal properties of various diagrams can be quite cumbersome. That said, we believe that it is still important to draw a contrast between both viewpoints in order to motivate the field of category theory. We focus our scope to the short five lemma, one of the more elementary diagram lemmas, and present a quick exposition on relevant subjects. Moreover, we give an original proof of the short five lemma using the universal property of pullbacks.
