Abstract
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH B over a fixed spaceB ([1]). They have introduced two pairs of adjoint functors:P B N B andm * m *, whereP B :H B →H B, andm *:H A →H B for a fixed mapm:A→B. We have introduced a split fibration of categoriesL:H b →H B and provedL J, J L in [2]. This paper first extendsP B N B to\(P_{\bar B} b_* \dashv N_B b^\# \) for any fixed mapb:\(B \to \bar B\). Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categoriesH b andH b whereH b is the dual ofH b . One of our results isN b P b . This differs fromP B N B .
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Supported by National Natural Science Foundation of China
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Jixiang, C. Some pairs of adjoint functors involving track homotopy categories. Acta Mathematica Sinica 14, 321–326 (1998). https://doi.org/10.1007/BF02580435
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DOI: https://doi.org/10.1007/BF02580435