Localisation homotopique et tour de Taylor pour une catégorie abélienne
HTML articles powered by AMS MathViewer
- by Olivier Renaudin PDF
- Trans. Amer. Math. Soc. 354 (2002), 75-89 Request permission
Abstract:
On indique comment une sous-catégorie colocalisante d’une catégorie abélienne induit une localisation dans la catégorie dérivé. Ceci permet une nouvelle construction de la tour de Taylor d’un foncteur à valeur dans une catégorie de module.References
- A. K. Bousfield, The localization of spaces with respect to homology, Topology 14 (1975), 133–150. MR 380779, DOI 10.1016/0040-9383(75)90023-3
- A. K. Bousfield, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77), no. 2, 207–220. MR 478159, DOI 10.1016/0022-4049(77)90067-6
- A. K. Bousfield, The localization of spectra with respect to homology, Topology 18 (1979), no. 4, 257–281. MR 551009, DOI 10.1016/0040-9383(79)90018-1
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- Albrecht Dold, Homology of symmetric products and other functors of complexes, Ann. of Math. (2) 68 (1958), 54–80. MR 97057, DOI 10.2307/1970043
- Albrecht Dold and Dieter Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier (Grenoble) 11 (1961), 201–312 (German, with French summary). MR 150183, DOI 10.5802/aif.114
- W.G. Dwyer, P. Hirshorn, D.M. Kan. Model Categories and More General Abstract Homotopy Theory. http://www-math.mit.edu/˜psh/
- W. G. Dwyer and J. Spaliński, Homotopy theories and model categories, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 73–126. MR 1361887, DOI 10.1016/B978-044481779-2/50003-1
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
- Vincent Franjou and Jeffrey H. Smith, A duality for polynomial functors, J. Pure Appl. Algebra 104 (1995), no. 1, 33–39. MR 1359689, DOI 10.1016/0022-4049(94)00115-Y
- Pierre Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448 (French). MR 232821, DOI 10.24033/bsmf.1583
- Brenda Johnson and Randy McCarthy, Taylor towers for functors of additive categories, J. Pure Appl. Algebra 137 (1999), no. 3, 253–284. MR 1685140, DOI 10.1016/S0022-4049(97)00203-X
- B. Johnson, R. McCarthy. Deriving calculus with cotriples. A paraitre dans Cahiers Topologies Geom. Differentielle Categ. http://www.math.uiuc.edu/˜randy/
- Nicholas J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra. II, $K$-Theory 8 (1994), no. 4, 395–428. MR 1300547, DOI 10.1007/BF00961409
- Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
- F. Morel, V. Voevodsky. $A^1$-homotopy theory of schemes, Inst. Hautes Études Sci. Math. No. 90, 45-143 (1999)
- C. Năstăsescu and B. Torrecillas, Colocalization on Grothendieck categories with applications to coalgebras, J. Algebra 185 (1996), no. 1, 108–124. MR 1409977, DOI 10.1006/jabr.1996.0315
- T. I. Pirashvili, Higher additivizations, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 91 (1988), 44–54 (Russian, with English summary). MR 1029006
- N. Popescu, Abelian categories with applications to rings and modules, London Mathematical Society Monographs, No. 3, Academic Press, London-New York, 1973. MR 0340375
- Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432, DOI 10.1007/BFb0097438
- B. Richter. Taylor towers for abelian $\Gamma$-groups. Prépublication, Université de Bonn (1999)
- Charles A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994. MR 1269324, DOI 10.1017/CBO9781139644136
Additional Information
- Olivier Renaudin
- Affiliation: Department of Mathematics, Aarhus University, 8000 Aarhus C, Denmark
- Email: renaudin@imf.au.dk
- Received by editor(s): November 14, 2000
- Published electronically: August 21, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 75-89
- MSC (2000): Primary 18E35, 18G55
- DOI: https://doi.org/10.1090/S0002-9947-01-02855-0
- MathSciNet review: 1859026