论文标题
保留订单的地图的量子
The quantale of order-preserving maps
论文作者
论文摘要
在本文中，在订单保存地图中定义了两个新的组成操作。他们可以像通常的组成操作一样对保留订单的地图行事。当订单保留地图是保留地图或Meet Presherving Maps时，它们与通常的组成操作相吻合。通常的构图操作不能赋予订单的$ l^{l} $在完整的晶格$ l $带有量子或共同量子结构上保存地图的$ l^{l} $。幸运的是，每当$ l $是完全分布的晶格时，两个新操作分别可以将$ l^{l} $赋予量子和共同量词结构。
In this paper, two new composition operations are defined among the order-preserving maps. They can act on order-preserving maps like the usual composition operation. They are coincide with the usual composition operation when the order-preserving maps are sup-preserving maps or meet-preserving maps. The usual composition operation can't endow the set $L^{L}$ of order preserving maps on a complete lattices $L$ with quantale or co-quantale structures. Luckily, two new operations can endow $L^{L}$ with a quantale and a co-quantale structures respectively, whenever $L$ is a completely distributive lattice.
