涉及迹同伦范畴的几对伴随函子

Ｋ．Ａ．Ｈａｒｄｉｅ与Ｋ．Ｈ．Ｋａｍｐｓ研究过固定空间Ｂ上的迹同伦范畴（［１］）．他们引进了两对伴随函子ＰＢ┤ＮＢ与ｍ┤ｍ，此处ｍ：ＡＢ是固定映射，ＰＢ：ＨＢＨＢ与ｍ：ＨＡＨＢ是函子．我们在［２］中引进了分裂的范畴纤维化Ｌ：ＨｂＨＢ，并且证明了Ｌ┤Ｊ，Ｊ┤Ｌ．本文首先将ＰＢ┤ＮＢ推广到ＰＢｂ┤ＮＢｂ＃，其中ｂ：ＢＢ是任一固定映射，并且我们还得到涉及迹同伦范畴Ｈｂ与Ｈｂ的两对伴随函子，此处Ｈｂ是Ｈｂ的对偶．特别，Ｎｂ┤Ｐｂ不同于ＰＢ┤ＮＢ．

Some Pairs of Adjoint Functors Involving Track Homotopy Categories

K.A. Hardie and K.H. Kamps investigated the track homotopy category H B over a fixed space B (). They have introduced two pairs of adjoint functors: P B┤N B and m *┤m *, where P B: H BH B and m *:H AH B for a fixed map m: AB. We have introduced a split fibration of categories L:H bH B and proved L┤J, J┤L in . This paper firstly extends P B┤N B to P b *┤N Bb # for any fixed map b: B. Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H b and H b where H b is the dual of H b.One of our results is N b┤P b. This differs from P B┤N B.