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Applied Categorical Structures

, Volume 4, Issue 2–3, pp 195–212 | Cite as

Categorical aspects of equivariant homotopy

  • Jean-Marc Cordier
  • Timothy Porter
Article

Abstract

We use the language of homotopy coherent ends and coends, and of homotopy coherent Kan extensions, to give enriched versions of results of Elmendorff. This enables a description of the homotopy type of the space of maps between two G-complexes to be given.

Mathematics Subject Classifications (1991)

18G55 18D20 55P91 

Key words

equivariant homotopy homotopy coherence orbit category enriched category theory 
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References

  1. 1.
    BournD. and CordierJ.-M.: A general formulation of homotopy limits, J. Pure Appl. Algebra 29 (1983), 129–141.Google Scholar
  2. 2.
    BousfieldA. K. and KanD. M.: Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer-Verlag, Berlin, 1972.Google Scholar
  3. 3.
    CordierJ.-M.: Sur la notion de diagramme homotopiquement cohérent, Cahiers Topologie Géom. Différentielle Catégoriques 23 (1982), 93–112.Google Scholar
  4. 4.
    Cordier, J.-M.: Extensions de Kan simplicialement cohérentes, Prépublications, Amiens, 1985.Google Scholar
  5. 5.
    CordierJ.-M.: Sur les limites homotopiques de diagrammes homotopiquement cohérents, Comp. Math. 62 (1987), 367–388.Google Scholar
  6. 6.
    CordierJ.-M. and PorterT.: Vogt's theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Philos. Soc. 100 (1986), 65–90.Google Scholar
  7. 7.
    Cordier, J.-M. and Porter, T.: Coherent Kan Extensions, (i). Simplicially Enriched Ends and Coends, U.C.N.W. Pure Maths., Preprint 86.19, 1986.Google Scholar
  8. 8.
    CordierJ.-M. and PorterT.: Fibrant diagrams, rectifications and a construction of Loday, J. Pure Appl. Algebra 67 (1990), 111–124.Google Scholar
  9. 9.
    Cordier, J.-M. and Porter, T.: Homotopy coherent category theory, Preprint, 1995.Google Scholar
  10. 10.
    DwyerW. G. and KanD. M., Singular functors and realization functors, Proc. Kon. Nederl. Akad. Wetensch. A87=Ind. Math. 46 (1984), 147–153.Google Scholar
  11. 11.
    ElmendorfA.: Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983), 275–284.Google Scholar
  12. 12.
    Kelly, G. M.: The Basic Concepts of Enriched Category Theory, LMS Lecture Notes 64, Cambridge University Press, 1983.Google Scholar
  13. 13.
    LückW.: Transformation Groups and Algebraic K-Theory, Lecture Notes in Math. 1408, Springer-Verlag, Berlin, 1989.Google Scholar
  14. 14.
    May, J. P.: Classifying spaces and fibrations, Mem. Amer. Math. Soc. 155 (1975).Google Scholar
  15. 15.
    MeyerJ.-P.: Bar and cobar constructions, I, J. Pure Appl. Algebra 33 (1984) 163–207.Google Scholar
  16. 16.
    MoerdijkI. and SvenssonJ.-A.: Algebraic classification of equivariant homotopy 2-types, J. Pure Appl. Algebra 89 (1993), 187–216.Google Scholar
  17. 17.
    SeymourR. M.: Some functorial constructions on G-spaces, Bull. London Math. Soc. 15 (1983), 353–359.Google Scholar
  18. 18.
    Tammo TomDieck: Transformation Groups, de Gruyter Studies in Mathematics, 8, de Gruyter, Berlin-New York, 1987.Google Scholar
  19. 19.
    VogtR. M.: Homotopy limits and colimits, Math. Z. 134 (1973), 11–52.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Jean-Marc Cordier
    • 1
  • Timothy Porter
    • 2
  1. 1.Faculté de Mathématiques ed d'InformatiqueUniversité de Picardie-Jules VerneAmiens Cédex 1France
  2. 2.School of MathematicsUniversity of WalesBangorWales, U.K.

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