论文标题
有限近似作为研究三角类别的工具
Finite approximations as a tool for studying triangulated categories
论文作者
论文摘要
小型有限的实体比巨大的无限实体更容易，更容易操纵。因此，大量数学的大部分专门用于减少对大型，繁琐的物体的研究，以分析其有限的构建块。这种一般模式的表现，在对派生和三角形类别的研究中，几乎可以追溯到主题的开始 - 更准确地说，是在1970年代初的SGA6中的Illusie的文章。 新的，至少在派生和三角构剖分类别的世界中的新事物是，从更仔细的分析和更精确地量化有限的物体可以估计无限对象的效率上，从而获得了额外的里程。这导致了三角形类别的指标的研究，并且可以通过有限尺寸的有限对象近似对象的准确性。
Small, finite entities are easier and simpler to manipulate than gigantic, infinite ones. Consequently huge chunks of mathematics are devoted to methods reducing the study of big, cumbersome objects to an analysis of their finite building blocks. The manifestation of this general pattern, in the study of derived and triangulated categories, dates back almost to the beginnings of the subject -- more precisely to articles by Illusie in SGA6, way back in the early 1970s. What's new, at least new in the world of derived and triangulated categories, is that one gets extra mileage from analysing more carefully and quantifying more precisely just how efficiently one can estimate infinite objects by finite ones. This leads one to the study of metrics on triangulated categories, and of how accurately an object can be approximated by finite objects of bounded size.
