Israel Journal of Mathematics

, Volume 48, Issue 4, pp 331–339 | Cite as

Mappings of bar constructions

  • Jean-Pierre Meyer


Quillen’s famous Theorem B describes the homotopy fiber ofBF :B C/arB, wheref :C is a functor andB the classifying space functor. This is here generalized to a description of the homotopy fiber ofB(F,α,β) :B(Y C,X)/ar(Y/t' C/t',X/t') where (F,α,β) : (Y C,X)/ar(Y/t' C/t',X/t') is a mapping of 2-sided bar construction data.


Geometric Realization Homotopy Equivalence Topological Category Simplicial Space Simplicial Homotopy 
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  1. 1.
    A. K. Bousfield and D. M. Kan,Homotopy limits, completions and localizations, Lecture Notes in Mathematics304, Springer-Verlag, Berlin, 1972.MATHGoogle Scholar
  2. 2.
    J. P. May,Classifying spaces and fibrations, Mem. Am. Math. Soc.,155 (1975).Google Scholar
  3. 3.
    J.-P. Meyer,Bar and cobar constructions I, J. Pure Appl. Alg., to appear.Google Scholar
  4. 4.
    J.-P. Meyer,Bar and cobar constructions II, in preparation.Google Scholar
  5. 5.
    J. Milnor,Construction of universal bundles, II, Ann of Math.63 (1956), 430–436.CrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Morava,Hypercohomology of topological categories, Proceedings, Evanston 1977, Lecture Notes in Mathematics658, Springer-Verlag, Berlin, 1978, pp. 383–403.Google Scholar
  7. 7.
    V. Puppe,A remark on “homotopy fibrations”, Manuscripta Math.12 (1974), 113–120.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    D. G. Quillen,Higher algebraic K-theory, I, Lecture Notes in Mathematics341, Springer-Verlag, Berlin, 1973, pp. 85–147.Google Scholar
  9. 9.
    G. Segal,Classifying spaces and spectral sequences, Pub. Math. I.H.E.S.34 (1968), 105–112.MATHGoogle Scholar
  10. 10.
    J. D. Stasheff,Associated fibre spaces, Mich. Math. J.15 (1968), 457–470.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    R. W. Thomason,Homotopy colimits in the category of small categories, Math. Proc. Camb. Phil. Soc.85 (1979), 91–109.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    K. A. Hardie,Quasifibration and adjunction, Pac. J. Math.35 (1970), 389–397.MATHMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1984

Authors and Affiliations

  • Jean-Pierre Meyer
    • 1
  1. 1.The Johns Hopkins UniversityBaltimoreUSA

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