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集合范畴上超滤函子的余代数 被引量：1

The Ultrafilter Functor on Set for Coalgebras
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摘要 定义了集合范畴上的超滤函子F_u(-),并研究了相关性质.包括函子F_u(-)在有限集上保拉回,一个集合的子集成为F_u-子余代数的充要条件,以及两个余代数之间的态射是F_u-余代数同态的充要条件,子集成为子余代数的充要条件,最后以拓扑空间作为F_u-余代数的具体实例,研究了拓扑空间的连续映射与超滤函子的余代数同态之间的关系. In this paper, we introduce ultrafilter functor Fu（-） on the category Set and discuss its properties. We get that the ultrafilter functor Fu（-） can preserve pullback on finite set. And we consider the necessary and sufficient conditions under which a subset is a Fu-subcoalgebra and a morphism is an Fu-coalgebra homomorphism. Finally, we take the topological spaces as an concrete example of the Fu-coalgebra to consider the relation
作者 郑艳霞 樊磊
机构地区 首都师范大学数学科学学院 首都师范大学教育技术系
出处 《数学的实践与认识》 CSCD 北大核心 2013年第6期246-250,共5页 Mathematics in Practice and Theory
关键词 超滤 函子 保拉回 余代数同态 ultrafilter functor pullback homomorphism of coalgebras
分类号 O153 [理学—基础数学]
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参考文献9

  • 1Aczel P. and Mendler N. A final coalgebra theorem[J]. Category Theory and Computer Sci- ence,1989(389) 357-365.
  • 2Rutten J J M M. Universal coalgebra:a theory of systerms[J]. Theoretical Computer Science, 2000(249): 3-80.
  • 3Gumm H P. Functors for coalgebras[J]. Algebra Universalis, 2000, 45(2-3): 135-147.
  • 4Engelking R. General Tooology[M], Warszawa, Polish, 1977.
  • 5Jech T. Set Theory [M]. The Third Millennium Edition,revised and expanded, Springer, 2006.
  • 6Jacobs B.Introduction to Coalgebras Towards Mathematics of States and Observations[M/OL].Book Draft, Available at http://www.cs.runl/ bart, 2005.
  • 7Gumm H P. Elements of the General Theory of Coalgebras[M/OL]. Lecture Notes, Rand Africans University, http://www.mathematik, uni-marburg.de/gumm/Papers/publ.html,1999.
  • 8Gumm H P, SchrSer T. Coalgebraic structure from weak limit preserving functors[J]. Electronic Notes in Theoretcial Computer Science, 2000(33): 111-131.
  • 9Hughes J, Jacobs B. Simulations in Coalgebra[M/OL]. http://www.cs.kun.nl/baxt, 2004.

同被引文献8

  • 1Rutten J J M M.Universal coalgebra:a theory of systems[J].Theoretical Computer Science,2000,249:3-80.
  • 2H.P.Gumm.Functors for coalgebras[J].Algebra Universalis,2001,45:135-147.
  • 3R.Engelking.General Topology[M].Warszawa,Polish,1977.
  • 4T.Jech.Set Theory[M].The Third Millennium Edition,revised and expanded,Springer,2006.
  • 5H.P.Gumm.Elements of the general theory of coalgebras[J].Lecture Notes,Rand Africans University,http://www.mathematik,uni-marburg.de/gumm/Papers/publ.html,1999.
  • 6B.Jacobs.Introduction to Coalgebras Towards Mathematics of States and Observations[J].Book Draft,Available at http://www.cs.runl/bart,2005.
  • 7S.MacLane.Categories for the Working Mathematicians[J].Springer-Verlag,Berlin.New York,He.idelberg,1971.
  • 8H.P.Gumm,T.Schr(o|¨)er.Coalgebraic structure from weak limit preserving functors[J].Electronic Notes in Theoretcial Computer Science,2000,33:111-131.

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数学的实践与认识
2013年 第6期

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