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Galois Connections in A Topos 被引量：6

Galois Connections in A Topos
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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. 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.
作者 Tao LU Wei HE Xi Juan WANG
机构地区 Department of Mathematics School of Mathematics and Computer Science Lianyungang Teacher's College
出处 《Journal of Mathematical Research and Exposition》 CSCD 2010年第3期381-389,共9页 数学研究与评论（英文版）
基金 Supported by the National Natural Science Foundation of China (Grant No.10731050)
关键词 partial order object Galois connection topos. partial order object Galois connection topos.
分类号 O153.1 [理学—基础数学] O154 [理学—基础数学]
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参考文献12

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同被引文献22

  • 1JOHNSTONE P T. Sketches of an Elephant: a topos theory compendium[ M ]. Oxford: Oxford University Press, 2002.
  • 2MAC LANE S, MOERDIJK L. Sheaves in geometry and logic : a first introduction to topos [ M ]. New York: Springer-Ver- lag, 1992.
  • 3MAC LANE S. Categories for working mathematician[M]. New York: Springer-Verlag, 1972.
  • 4JOHNSTONE P T, JOYAL A. Continuous categories and exponentiable toposes [ J ]. Journal olr Pure and Apphed Algebra, 1982, 25:255-296.
  • 5KOCK A, LECOUTURIER P, MIKKELSEN C J. Some topos theoretic concepts of finiteness[ M]//Lecture Notes in Math. Berlin: Springer-Vedag, 1975, 445:209-283.
  • 6LUO Maokang, HE Wei. A new logic for uncertainty[J]. 2015, http://arxiv, org/abs/1506. 03123.
  • 7JOHNSTONE P T. Sketches of an elephant: A topos theory compendium[M]. Oxford:Oxford University Press, 2002.
  • 8MAC LANE S, MOERDIJK L. Sheaves in Geometry and Logic: A first introduction to topos[M]. New York Springer-Verlag, 1992.
  • 9MAC LANE S. Categories for working mathematician[M]. New York:Springer-Verlag,1972.
  • 10JOHNSTONE P T, JOYAL A. Continuous categories and exponentiable toposes[J]. Journal of Pure and Applied Algebra, 1982,25 : 255 - 296.

引证文献6

二级引证文献10

Journal of Mathematical Research and Exposition
2010年 第3期

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