Some functors on Grothendieck exact sequences of type I

C. L. SHARMA

doi:10.2969/jmsj/02810212

C. L. SHARMA

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ジャーナルフリー

1976 年 28 巻 1 号 p. 212-221

DOI https://doi.org/10.2969/jmsj/02810212

詳細

Published: 1976 Received: 1973/10/20 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文抄録訂正内容: Right : It has been shown that the exactness of Grothendieck exact sequences of type I, of abelian groups and their homomorphisms is preserved by the free functor F, the polynomial functors P_n, the n-th symmetric product functors Spⁿ, and the direct limit functor lim_→. A necessary and sufficient condition has also been sought under which the polynomial functors Q_n preserve the exactness of Grothendieck exact sequences of type I.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Barr, Lecture Notes in Mathematics, No. 236, Springer-Verlag.
2) A. Dold, Homology of symmetric products and other functions of complexes, Ann. of Math., 68 (1958), 54-80.
3) M. Mitchell, Theories of Categories, Academic Press, New York and London, 1965.
4) I. B. S. Passi, Polynomial maps on groups, J. Algebra, 9 (1968), 121-150.
5) I. B.S. Passi, Polynomial functors, Proc. Cambridge Philos. Soc., 66 (1968), 505.
6) M. N. Roby, Lois Pólynomes et Lois formelles en théorie des modules, Ann. Sci. Ecole Normale Superieure, (1963).
7) L. R. Vermani, Nilpotent groups, Ph. D. Thesis, The Kurukshetra University, Kurukshetra.

Right : [1] M. Barr, Lecture Notes in Mathematics, No. 236, Springer-Verlag.
[2] A. Dold, Homology of symmetric products and other functions of complexes, Ann. of Math., 68 (1958), 54-80.
[3] M. Mitchell, Theories of Categories, Academic Press, New York and London, 1965.
[4] I. B. S. Passi, Polynomial maps on groups, J. Algebra, 9 (1968), 121-150.
[5] I. B. S. Passi, Polynomial functors, Proc. Cambridge Philos. Soc., 66 (1968), 505.
[6] M. N. Roby, Lois Pólynomes et Lois formelles en théorie des modules, Ann. Sci. Ecole Normale Superieure, (1963).
[7] L. R. Vermani, Nilpotent groups, Ph. D. Thesis, The Kurukshetra University, Kurukshetra.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

抄録

It has been shown that the exactness of Grothendieck exact sequences of type I, of abelian groups and their homomorphisms is preserved by the free functor F, the polynomial functors P_n, the n-th symmetric product functors Spⁿ, and the direct limit functor lim_→. A necessary and sufficient condition has also been sought under which the polynomial functors Q_n preserve the exactness of Grothendieck exact sequences of type I.

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