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Connected sequences of stable derived functors and their applications

Seria
Rozprawy Matematyczne tom/nr w serii: 111 wydano: 1974
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Abstrakty
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CONTENTS
1. Introduction........................................................................................................................................................................................................ 5
2. Category of complexes.................................................................................................................................................................................... 7
3. Left stable derived functors of covariant functors....................................................................................................................................... 11
4. Functors with, extensions............................................................................................................................................................................... 24
5. On the exactness of connected sequences................................................................................................................................................ 37
6. Right and left stable derived functors of contravariant functors. Right stable derived functors of covariant functors................... 39
7. Symmetric power functor $SP^n$ and exterior power functor $Λ^n$..................................................................................................... 43
8. On J. H. C. Whitehead's functor Γ.................................................................................................................................................................. 48
9. Computation of the modules $L^s_qSP^2(R)$, $L^s_qΛ^2(R)$ and $L^s_qΓ(R)$........................................................................... 53
10. Computation of the functors $L^s_qSP^2$, $L^s_qΛ^2$ and $L^s_qΓ$............................................................................................ 59
11. Eilenberg-MacLane's stable homology and cohomology functors...................................................................................................... 64
References............................................................................................................................................................................................................ 67
Słowa kluczowe
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Miejsce publikacji
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 111
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXI
Daty
wydano
1974
Twórcy
  • Institute of Mathematics, N. Copernicus University, Toruń (Instytut Matematyki, Uniwersytet M. Kopernika, Toruń)
autor
  • Institute of Mathematics, Polish Academy of Sciences (Instytut Matematyczny, PAN)
Bibliografia
  • [1] H. Cartan, et al., Algèbres d'Eilenberg-MacLane et homotopie, Sommaire Henri Cartan de l'Ecole Normale Supérieure, 7e année (1954/55), 2 ème éd.. Secretariat mathématique, 11 rue Pierre Curie, 1956.
  • [2] H. Cartan, S. Eilenberg, Homological algebra, Princeton 1956.
  • [3] A. Dold, Homology of symmetric product and other functors of complexes, Ann. of Math. 68 (1958), pp. 54-80.
  • [4] A. Dold, Zur Homotopietheorie der Kettenkomplexe, Math. Ann. 140 (1960), pp. 278-298.
  • [5] A. Dold, D. Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier 11 (1961), pp. 201-312.
  • [6] S. Eilenberg, S. MacLane, On the groups H(π,n), I, Ann., of Math. 58 (1953), pp. 55-106.
  • [7] S. Eilenberg, On the groups H(π,n), II, Ann. of Math. 60 (1954), pp. 49-139.
  • [8] S. Eilenberg, N. Steenrod, Foundations of algebraic topology, Princeton 1952.
  • [9] R. Hartshorne, Residues and duality, Lecture Notes in Mathematics, 20,, Berlin-Heidelberg-New York 1966.
  • [10] G. H. Kelley, Single-space axioms for homology theory, Proc, Cambridge Phil. Soc. 55 (1959), pp. 10-23.
  • [11] D. Lazard, Sur les modules plats, C. R. Acad. Sc. Paris 258 (1964), pp. 6313-6316.
  • [12] S. MacLane, Homology, Berlin-Götingen-Heidelberg 1963.
  • [13] D. Simson, A. Tyc, On stable derived functors, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 18 (1970), pp. 57—64.
  • [14] D. Simson, A. Tyc,, On stable derived functors, II, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 18 (1970), pp. 635-639.
  • [15] J. H. C. Whitehead, A certain exact sequence, Ann. of Math. 52 (1960), pp. 51-108.
  • [16] G. W. Whitehead, Generalised homology theories, Trans. Amer. Math. Soc. 102 (1962), pp. 227-283.
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