精确结构的约化
Reduction of exact structures
摘要：
表示论中的正合范畴的例子有拟遗传代数上的Delta滤模范畴，也有与矩阵问题相关的各种范畴，如偏序集表示或bocses表示。本文以矩阵问题为背景，研究了正合结构的约化问题，并考虑了固定可加范畴A上所有正合结构的偏序集Ex（A）。这个偏序集是一个完全格，在适当的条件下，Enomoto的结果意味着它是布尔的。本文通过推广阿贝尔范畴的概念，如对象相对于E的长度和正合范畴（A，E）的长度，对正合结构E进行了详细的研究。我们研究了（A，E）的Gabriel-Roiter测度，并进一步研究了当精确结构变化时这些概念如何变化。
英文摘要：
Examples of exact categories in representation theory are given by the category of Delta-filtered modules over quasi-hereditary algebras, but also by various categories related to matrix problems, such as poset representations or representations of bocses. Motivated by the matrix problem background, we study in this article the reduction of exact structures, and consider the poset Ex(A) of all exact structures on a fixed additive category A. This poset turns out to be a complete lattice, and under suitable conditions results of Enomoto's imply that it is boolean. We initiate in this article a detailed study of exact structures E by generalizing notions from abelian categories such as the length of an object relative to E and the quiver of an exact category (A,E). We investigate the Gabriel-Roiter measure for (A,E), and further study how these notions change when the exact structure varies.
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