We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In parti...We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.展开更多
K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). 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 ...K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). 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 [2]. This paper first 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.展开更多
基金supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project(707004)the Doctorate Program FOUNDATION(20040027002)Ministry of Education of China,The partial support from NSF of China is also acknowledged
文摘We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
基金Supported by National Natural Science Foundation of China
文摘K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). 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 [2]. This paper first 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.
