论文标题
晶格的规范扩展不仅仅是完美的
Canonical extensions of lattices are more than perfect
论文作者
论文摘要
在\ cite {cgh15}中，我们引入了TIRS图和TIRS框架，以创建一个新的自然设置，以供晶格的规范扩展。在\ cite {cgh15}的延续中，我们通过表征对TIRS框架的完美晶格（因此以及TIRS图）来回答问题2。我们介绍了一个新的名为PTI Lattices的完美晶格的子类，并表明晶格的规范扩展是PTI晶格，而“不仅仅是完美的格子”。我们介绍了TIRS结构的形态，并将TIRS图和TIR框架之间的对应关系从\ cite {CGH15}放入一个完整的分类框架中。我们通过示例说明了Perfects Lattices类别和TIR类别的类别之间的对应关系。
In \cite{CGH15} we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. In this continuation of \cite{CGH15} we answer Problem 2 from there by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are `more' than just perfect lattices. We introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames from \cite{CGH15} into a full categorical framework. We illustrate our correspondences between classes of perfects lattices and classes of TiRS graphs by examples.
