偏序范畴若干问题研究

Some Researches of Poset Category

本文介绍了关系及关系矩阵等概念,并着重讨论了偏序关系及对应的偏序范畴、偏序矩阵,刻划了偏序范畴的始对象、终对象和零对象,偏序范畴的积范畴以及给出相应的矩阵的关系,即积范畴对应的偏序矩阵是原来两个偏序矩阵的张量积;讨论了等价的偏序范畴对应的偏序集之间的关系.

This paper introduces some concepts, such as the concept of the relation, relation matrix, etc. It focuses on the discussions of the poset, the corresponding poset category and poset matrix and describes the initial object, terminal object and zero object, the product category of poset categories. Then it gives the relationship of the corresponding poset matrix, i.e. the poser matrix of the product categories identifies with the tensor product of two original poset matrixes and discusses the relations of the corresponding posets of two equivalent poset categories.