Direct limits and inverse limits of Mackey functors
Let G be a finite group, S the subgroup category of G, and M a Mackey functor on G. For full subcategories G and H of S, we have the direct limit M⁎(G) and the inverse limit M⁎(H) of M. In this paper we study relation between the canonical homomorphisms ind:M⁎(G)→M(G) and res:M(G)→M⁎(H).
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| Published in | Journal of algebra Vol. 470; pp. 68 - 76 |
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| Format | Journal Article |
| Language | English |
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Elsevier Inc
15.01.2017
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| Abstract | Let G be a finite group, S the subgroup category of G, and M a Mackey functor on G. For full subcategories G and H of S, we have the direct limit M⁎(G) and the inverse limit M⁎(H) of M. In this paper we study relation between the canonical homomorphisms ind:M⁎(G)→M(G) and res:M(G)→M⁎(H). |
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| AbstractList | Let G be a finite group, S the subgroup category of G, and M a Mackey functor on G. For full subcategories G and H of S, we have the direct limit M⁎(G) and the inverse limit M⁎(H) of M. In this paper we study relation between the canonical homomorphisms ind:M⁎(G)→M(G) and res:M(G)→M⁎(H). |
| Author | Morimoto, Masaharu |
| Author_xml | – sequence: 1 givenname: Masaharu surname: Morimoto fullname: Morimoto, Masaharu email: morimoto@ems.okayama-u.ac.jp organization: Department of Mathematics, Graduate School of Natural Science and Technology, Okayama University, 3–1–1 Tsushimanaka, Kitaku, Okayama, 700-5360 Japan |
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| Keywords | secondary Mackey functor Burnside ring Green ring functor primary |
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| References | tom Dieck (br0040) 1987; vol. 8 Ju, Matsuzaki, Morimoto (br0080) 2003; 29 Dress (br0060) 1975; 102 Oliver (br0110) 1975; 50 Yoshida (br0120) 1983; 80 Bak (br0020) 1995; 104 Dress (br0050) 1969; 110 Bak (br0010) 1981; vol. 98 tom Dieck (br0030) 1979; vol. 766 Gluck (br0070) 1981; 25 Morimoto (br0100) 2002 Kratzer, Thévenaz (br0090) 1984; 59 Gluck (10.1016/j.jalgebra.2016.09.002_br0070) 1981; 25 Kratzer (10.1016/j.jalgebra.2016.09.002_br0090) 1984; 59 Dress (10.1016/j.jalgebra.2016.09.002_br0050) 1969; 110 Yoshida (10.1016/j.jalgebra.2016.09.002_br0120) 1983; 80 Dress (10.1016/j.jalgebra.2016.09.002_br0060) 1975; 102 Oliver (10.1016/j.jalgebra.2016.09.002_br0110) 1975; 50 tom Dieck (10.1016/j.jalgebra.2016.09.002_br0030) 1979; vol. 766 Bak (10.1016/j.jalgebra.2016.09.002_br0010) 1981; vol. 98 Ju (10.1016/j.jalgebra.2016.09.002_br0080) 2003; 29 Morimoto (10.1016/j.jalgebra.2016.09.002_br0100) 2002 tom Dieck (10.1016/j.jalgebra.2016.09.002_br0040) 1987; vol. 8 Bak (10.1016/j.jalgebra.2016.09.002_br0020) 1995; 104 |
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Math. contributor: fullname: Gluck – volume: vol. 766 year: 1979 ident: 10.1016/j.jalgebra.2016.09.002_br0030 article-title: Transformation Groups and Representation Theory contributor: fullname: tom Dieck – volume: 50 start-page: 155 year: 1975 ident: 10.1016/j.jalgebra.2016.09.002_br0110 article-title: Fixed point sets of groups on finite acyclic complexes publication-title: Comment. Math. Helv. doi: 10.1007/BF02565743 contributor: fullname: Oliver – volume: 104 start-page: 235 year: 1995 ident: 10.1016/j.jalgebra.2016.09.002_br0020 article-title: Induction for finite groups revisited publication-title: J. Pure Appl. Algebra doi: 10.1016/0022-4049(94)00137-5 contributor: fullname: Bak – volume: 59 start-page: 425 year: 1984 ident: 10.1016/j.jalgebra.2016.09.002_br0090 article-title: Fonction de Möbius d'un groupe fini et anneau de Burnside publication-title: Comment. Math. Helv. doi: 10.1007/BF02566359 contributor: fullname: Kratzer – volume: vol. 8 year: 1987 ident: 10.1016/j.jalgebra.2016.09.002_br0040 article-title: Transformation Groups contributor: fullname: tom Dieck – volume: 80 start-page: 90 year: 1983 ident: 10.1016/j.jalgebra.2016.09.002_br0120 article-title: Idempotents of Burnside rings and Dress induction theorem publication-title: J. Algebra doi: 10.1016/0021-8693(83)90019-4 contributor: fullname: Yoshida – volume: 102 start-page: 291 year: 1975 ident: 10.1016/j.jalgebra.2016.09.002_br0060 article-title: Induction and structure theorems for orthogonal representations of finite groups publication-title: Ann. of Math. doi: 10.2307/1971033 contributor: fullname: Dress – volume: 25 start-page: 63 year: 1981 ident: 10.1016/j.jalgebra.2016.09.002_br0070 article-title: Idempotnent formula for the Burnside algebra with applications to the p-subgroup simplicial complex publication-title: Illinois J. Math. doi: 10.1215/ijm/1256047365 contributor: fullname: Gluck – volume: 110 start-page: 213 year: 1969 ident: 10.1016/j.jalgebra.2016.09.002_br0050 article-title: A characterization of solvable groups publication-title: Math. Z. doi: 10.1007/BF01110213 contributor: fullname: Dress – start-page: 129 year: 2002 ident: 10.1016/j.jalgebra.2016.09.002_br0100 article-title: The Burnside ring revisited contributor: fullname: Morimoto – volume: vol. 98 year: 1981 ident: 10.1016/j.jalgebra.2016.09.002_br0010 article-title: K-Theory of Forms contributor: fullname: Bak – volume: 29 start-page: 285 year: 2003 ident: 10.1016/j.jalgebra.2016.09.002_br0080 article-title: Mackey and Frobenius structures on odd dimensional surgery obstruction groups publication-title: K-Theory doi: 10.1023/B:KTHE.0000009976.01677.17 contributor: fullname: Ju |
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| Snippet | Let G be a finite group, S the subgroup category of G, and M a Mackey functor on G. For full subcategories G and H of S, we have the direct limit M⁎(G) and the... |
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| Title | Direct limits and inverse limits of Mackey functors |
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