Some pairs of adjoint functors involving track homotopy categories |
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| Authors: | Chen Jixiang |
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| Affiliation: | (1) Department of Mathematics, Nankai University, 300071 Tianjin, China |
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| 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  for any fixed mapb:  . 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 . Supported by National Natural Science Foundation of China |
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| Keywords: | Track homotopy category Fibration of categories Adjoint functor |
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