| 集合范畴上超滤函子的余代数 |
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| 引用本文： | 郑艳霞,樊磊.集合范畴上超滤函子的余代数[J].数学的实践与认识,2013,43(6). |
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| 作者姓名： | 郑艳霞 樊磊 |
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| 作者单位： | 1. 首都师范大学数学科学学院,北京,100048
2. 首都师范大学教育技术系,北京,100048 |
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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.
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| 关 键 词： | 超滤 函子 保拉回 余代数同态 |
The Ultrafilter Functor on Set for Coalgebras |
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| ZHENG Yan-xia
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FAN Lei.The Ultrafilter Functor on Set for Coalgebras[J].Mathematics in Practice and Theory,2013,43(6). |
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| Authors: | ZHENG Yan-xia FAN Lei |
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| Abstract: | In this paper,we introduce ultrafilter functor F_u(-) on the category Set and discuss its properties.We get that the ultrafilter functor F_u(-) can preserve pullback on finite set.And we consider the necessary and sufficient conditions under which a subset is a F_u-subcoalgebra and a morphism is an F_u -coalgebra homomorphism.Finally,we take the topological spaces as an concrete example of the F_u-coalgebra to consider the relation |
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| Keywords: | ultrafilter functor pullback homomorphism of coalgebras |
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