论文标题
有限posets和二元性的逆弗拉斯西式限制的POSET和格
An inverse Fraïssé limit for finite posets and duality for posets and lattices
论文作者
论文摘要
我们将所有有限部分订购的类别视为箭头，并在此类别中构造fraïssé序列。然后，我们使用部分顺序和晶格之间的众所周知的关系来构建与之相关的一系列晶格。这两个序列中的每个序列都有一个极限对象 - 一个逆极限，这也是我们感兴趣的对象。 在第一章中，有一些初步考虑部分订单，晶格，拓扑，倒数限制，类别理论和Fraïssé理论，这些理论将在以后使用。在第二章中，我们的结果考虑了有限poset类别的Fraïssé序列，并具有该序列的逆极限的商图和属性。在第三章中，我们研究了与它们相对应的POSET和秩序理想之间的联系，并获得了这些理想的感应序列。然后，我们研究该序列的逆极限的性质。
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fraïssé sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of lattices associated with it. Each of these two sequences has a limit object -- an inverse limit, which is an object of our interest as well. In the first chapter there are some preliminaries considering partial orders, lattices, topology, inverse limits, category theory and Fraïssé theory, which are used later. In the second chapter there are our results considering a Fraïssé sequence in category of finite posets with quotient maps and properties of inverse limit of this sequence. In the third chapter we investigate connections between posets and order ideals corresponding to them, getting an inductive sequence made of these ideals; then we study properties of the inverse limit of this sequence.
