拓扑空间偶范畴中的同伦正则态射
On Homotopy Regular Morphism in the Category of Topological Pairs

作者: 钱有华 * , 平 麟 , 陈胜敏 :浙江师范大学数理与信息工程学院;

关键词: 拓扑空间偶范畴同伦单(满)态射同伦正则态射标准分解The Category of Topological Pairs Homotopy Monomorphism (Epimorphism) Homotopy Regular Morphism Standard Decomposition

摘要:
本文将点标拓扑空间范畴中的同伦单、同伦满和同伦正则态射等概念推广到拓扑空间偶范畴的情形。研究了在中,同伦正则态射存在的条件、性质以及它与同伦单()态和同伦等价之间的关系。

Abstract:
In this paper, the concepts of homotopy monomorphism (epimorphism) and homotopy regular morphism in the category of topological space with base point are generalized to the category of topological pairs . The paper studies the conditions and properties of homotopy regular morphism and the relationships between homotopy monomorphism (epimorphism) and homotopy equivalent morphism in .

文章引用: 钱有华 , 平 麟 , 陈胜敏 (2013) 拓扑空间偶范畴中的同伦正则态射。 理论数学, 3, 14-17. doi: 10.12677/PM.2013.31004

参考文献

[1] S. T. Hu. Homotopy theory. New York: Academic Press, 1959.

[2] P. Hilton. Homotopy theory and duality. New York: Gorelen and Breach, 1965.

[3] T. Ganea. On monomorphisms in homotopy theory. Topology, 1976, 6 (2): 149-152.

[4] M. Mather. Homotopy monomorphisms and homotopy pushouts. Topology and its Applications, 1997, 81(2): 159-162.

[5] G. Mnklerjee. Equivalent homotopy epimorphisms homotopy monomorphisms and homotopy equivalence. Bulletin of the Belgian Mathemati- cal Society, 1995, 2(4): 447-461.

[6] W. H. Shen, Z. S. Zou. Semilocalization of epimorphisms and monomorphisms in homotopy theory. Topology and Its Applications, 1998, 88(3): 207-217.

[7] 冯良贵. 因式分解范畴[J]. 数学研究与评论, 1996, 16(2): 281-284.

[8] 曹永知, 郭驼英, 朱萍. 关于同伦正则态射[J]. 数学物理学报, 2000, 20(2): 274-277.

[9] 钱丽华, 钱有华. 同伦正则态射的注记[J]. 宁波大学学报(理工版), 2005, 18(4): 428-431.

[10] 王凯华, 陈胜敏, 钱有华. 同伦正则态射的若干性质[J]. 浙江师范大学学报(自然科学版), 2006, 29(3): 258-261.

[11] 钱有华, 陈胜敏. 同纬映象函子与同伦正则态射[J]. 吉林大学学报(理学版), 2009, 47(3): 476-480.

[12] 王向辉, 王玉玉. 有限CW复形间的稳定同伦正则态射[J]. 南开大学学报(自然科学版), 2011, 44(5): 34-40.

[13] 沈信耀. 同调论[M]. 北京: 科学出版社, 2002.

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