基于超图范畴积的同伦和Hom-构造  

Homotopy and Hom-Construction Based on Categorical Product of Hypergraphs

作　　者：张丛磊 赵彦 张志国[3] Zhang Conglei;Zhao Yan;Zhang Zhiguo(Department of Basic Science,Shanxi Agricultural University,Jinzhong 030801,China;School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,China;School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030031,China)

机构地区：[1]山西农业大学基础部,山西晋中030801 [2]河北地质大学数理教学部,河北石家庄050031 [3]山西师范大学数学与计算机科学学院,山西太原030031

出　　处：《南开大学学报（自然科学版）》2024年第4期25-30,共6页Journal of Nankai University(Natural Sience)

基　　金：国家自然科学基金面上项目(11771116);山西省高等学校科技创新项目(2022L266);山西省高等学校教学改革创新项目(J20220287,J20230594)。

摘　　要：基于超图范畴积引入了一类Hom-构造,并证明了范畴积运算在相应的Hom-构造下的相互作用良好.接着讨论了该Hom-构造与丘成桐先生等定义的超图同态同伦的关系,从拓扑的角度给出了丘成桐等人定义的超图同态同伦的必要条件.A Hom-construction associated to the categorical product of hypergraphs is introduced.It's shown that the categorical product operation interacts well with corresponding Hom-constructions.Then the relations between Hom-construction and the homotopy of hypergraph homomorphisms defined by Shing-Tung Yau et al are studied.A necessary condition of the homotopy of hypergraph homomorphisms from the view of topology is provided.

关 键 词：拓扑同伦 Hom-构造 超图同态同伦 超图的范畴积 强形变收缩核 

分 类 号：O189.2[理学—数学]