Topos中的Galois联络

Galois Connections in A Topos

中文关键词:  偏序对象  Galois联络.

英文关键词:partial order object  Galois connection  topos.

中文摘要:

      本文研究了任意 Topos 中的Galois 联络, 利用图表的方法证明了类似于经典序理论中的 Galois联络的一些好的等价刻画和性质, 从而表明在任意一个 Topos中可以利用图表方法来重新构建经典序理论.

英文摘要:

      In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.