Topos中完备偏序对象上的算子理论

doi:10.6040/j.issn.1671-9352.0.2015.481

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 64-71.doi: 10.6040/j.issn.1671-9352.0.2015.481

Topos中完备偏序对象上的算子理论

卢涛¹,王习娟^2*,贺伟³

1.淮北师范大学数学科学学院, 淮北安徽 235000;2.南京大学数学系, 南京江苏 210097;3.南京师范大学数学科学学院, 南京江苏210097

收稿日期:2015-10-15 出版日期:2016-02-16 发布日期:2016-03-11
通讯作者: 王习娟(1969— ), 女, 博士, 副教授, 研究方向为domain理论, 范畴论. E-mail:wangxijuan69@163.com E-mail:lutao7@live.com
作者简介:卢涛(1974— ), 男, 博士, 副教授, 研究方向为topos理论, 范畴论, locle理论. E-mail:lutao7@live.com
基金资助:
国家自然科学基金资助项目(11171156);安徽省高校自然科学研究重点项目(KJ2015A064)

The operator theory on complete partially ordered objects in a topos

LU Tao¹, WANG Xi-juan^2*, HE Wei³

1. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China;
2. Department of mathematics, Nanjing University, Nanjing 210097, Jiangsu;
China;
3. School of Mathematical Science, Nanjing Normal University, Nanjing 210097, Jiangsu, China

Received:2015-10-15 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 研究了完备偏序对象间的投射算子, 给出了闭包算子和核算子的等价刻画, 将一些格论中的经典结论推广到了topos中。

关键词: 核算子, 投射算子, 完备偏序对象, 闭包算子, 偏序对象

Abstract: The concept of the projective operators between complete partially ordered objects in a topos is investigated. The characterizations of the closure operator and the kernel operator in a topos are given, which are common generalizations of the classical lattice theory.

Key words: partially ordered object, projective operator, complete partially ordered object, closure operator, kernel operator

中图分类号:

O189.11

卢涛,王习娟,贺伟. Topos中完备偏序对象上的算子理论[J]. 山东大学学报（理学版）, 2016, 51(2): 64-71.

LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71.

参考文献

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Topos中完备偏序对象上的算子理论

The operator theory on complete partially ordered objects in a topos

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