Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SELF-PAIR HOMOTOPY EQUIVALENCES RELATED TO CO-VARIANT FUNCTORS

  • Ho Won Choi (Faculty of Liberal Arts and Teaching Kangnam University) ;
  • Kee Young Lee (Division of Applied Mathematical Sciences Korea University) ;
  • Hye Seon Shin (Division of Applied Mathematical Sciences Korea University)
  • Received : 2023.01.19
  • Accepted : 2024.01.23
  • Published : 2024.05.01
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Abstract

The category of pairs is the category whose objects are maps between two based spaces and morphisms are pair-maps from one object to another object. To study the self-homotopy equivalences in the category of pairs, we use covariant functors from the category of pairs to the group category whose objects are groups and morphisms are group homomorphisms. We introduce specific subgroups of groups of self-pair homotopy equivalences and put these groups together into certain sequences. We investigate properties of these sequences, in particular, the exactness and split. We apply the results to two special functors, homotopy and homology functors and determine the suggested several subgroups of groups of self-pair homotopy equivalences.

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Acknowledgement

The first-named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2022R1I1A1A01053856). The second-named author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2021R1F1A1048686). The third-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A6A3A01100186).

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