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Categorical aspects of equivariant homotopy

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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.

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References

  1. BournD. and CordierJ.-M.: A general formulation of homotopy limits, J. Pure Appl. Algebra 29 (1983), 129–141.

    Google Scholar 

  2. BousfieldA. K. and KanD. M.: Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer-Verlag, Berlin, 1972.

    Google Scholar 

  3. CordierJ.-M.: Sur la notion de diagramme homotopiquement cohérent, Cahiers Topologie Géom. Différentielle Catégoriques 23 (1982), 93–112.

    Google Scholar 

  4. Cordier, J.-M.: Extensions de Kan simplicialement cohérentes, Prépublications, Amiens, 1985.

  5. CordierJ.-M.: Sur les limites homotopiques de diagrammes homotopiquement cohérents, Comp. Math. 62 (1987), 367–388.

    Google Scholar 

  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. 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.

  8. CordierJ.-M. and PorterT.: Fibrant diagrams, rectifications and a construction of Loday, J. Pure Appl. Algebra 67 (1990), 111–124.

    Google Scholar 

  9. Cordier, J.-M. and Porter, T.: Homotopy coherent category theory, Preprint, 1995.

  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. ElmendorfA.: Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983), 275–284.

    Google Scholar 

  12. Kelly, G. M.: The Basic Concepts of Enriched Category Theory, LMS Lecture Notes 64, Cambridge University Press, 1983.

  13. LückW.: Transformation Groups and Algebraic K-Theory, Lecture Notes in Math. 1408, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  14. May, J. P.: Classifying spaces and fibrations, Mem. Amer. Math. Soc. 155 (1975).

  15. MeyerJ.-P.: Bar and cobar constructions, I, J. Pure Appl. Algebra 33 (1984) 163–207.

    Google Scholar 

  16. MoerdijkI. and SvenssonJ.-A.: Algebraic classification of equivariant homotopy 2-types, J. Pure Appl. Algebra 89 (1993), 187–216.

    Google Scholar 

  17. SeymourR. M.: Some functorial constructions on G-spaces, Bull. London Math. Soc. 15 (1983), 353–359.

    Google Scholar 

  18. Tammo TomDieck: Transformation Groups, de Gruyter Studies in Mathematics, 8, de Gruyter, Berlin-New York, 1987.

    Google Scholar 

  19. VogtR. M.: Homotopy limits and colimits, Math. Z. 134 (1973), 11–52.

    Google Scholar 

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Cordier, JM., Porter, T. Categorical aspects of equivariant homotopy. Appl Categor Struct 4, 195–212 (1996). https://doi.org/10.1007/BF00122252

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