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The milgram bar construction as a tensor product of functors

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Bibliography

  1. Cartan, H. Sur les groupes d'Eilenberg-Mac Lane H(π, n): I, II, Proc. Nat. Acad. Sci. USA 40 (1954), 467–471, 704–707.

    Article  MathSciNet  Google Scholar 

  2. Clark, Allen, Categorical Constructions in Topology, (Preprint, 1969).

    Google Scholar 

  3. Day, B.J. and Kelly, G.M. Enriched Functor Categories, Reports of the Midwest Category Seminar III, Berlin, Heidelberg, New York (Springer) 1969, pp. 178–191.

    Book  Google Scholar 

  4. Dold, A. and Lashof, R. Principal Quasifibrations and Fiber Homotopy Equivalence of Bundles, Ill. J. Math 3 (1959), 285–305.

    MathSciNet  MATH  Google Scholar 

  5. Dubuc, E. Kan Extensions in Enriched Category Theory. Forthcoming in Springer Lecture Notes Series.

    Google Scholar 

  6. Eilenberg, S. and Kelly, G. M. A Generalization of the Functorial Calculus, Journal of Algebra 1 (1964), 397–402.

    Article  MathSciNet  Google Scholar 

  7. Eilenberg, S. and Mac Lane, S. On the Groups H(π, n), I, II. Ann. of Math. 58 (1953), 55–106 and 60 (1954), 49–139.

    Article  MathSciNet  Google Scholar 

  8. Freyd, P. Abelian Categories, An Introduction to the Theory of Functors, New York (Harper and Row), 1963.

    MATH  Google Scholar 

  9. Kan, D.M. Adjoint Functors. Trans. Amer. Math. Soc. 87 (1958), 294–329.

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, Functors Involving C.S.S. Complexes, Trans. Amer. Math. Soc. 87 (1958), 330–346.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mac Lane, Saunders. Categorical Algebra, Bull. Amer. Math. Soc. 71 (1965), 40–106.

    Article  MathSciNet  MATH  Google Scholar 

  12. _____, Homology, Heidelberg and New York (Springer), 1963.

    Book  MATH  Google Scholar 

  13. Milgram, R.J. The Bar Construction and Abelian H-Spaces. Ill. J. Math. 11 (1967), 242–250.

    MathSciNet  MATH  Google Scholar 

  14. Rothenberg, M. and Steenrod, N.E. The Cohomology of Classifying Spaces and H-Spaces. Bull. Amer. Math. Soc. 71 (1965), 872–875.

    Article  MathSciNet  MATH  Google Scholar 

  15. Steenrod, N.E. A Convenient Category of Topological Spaces, Mich. Math. J. 14 (1967), 132–152.

    MathSciNet  MATH  Google Scholar 

  16. _____, Milgram's Classifying Space of a Topological Group. Topology, 7 (1968), 319–368.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ulmer, F. Representable Functors with Values in Arbitrary Categories. Journal of Algebra 8 (1968), 96–129.

    Article  MathSciNet  MATH  Google Scholar 

  18. Yoneda, N. On Ext and Exact Sequences. Jour. Fac. Sci., Univ. Tokyo 8 (1960), 507–576.

    MathSciNet  MATH  Google Scholar 

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F. P. Peterson

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© 1970 Springer-Verlag

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Mac Lane, S. (1970). The milgram bar construction as a tensor product of functors. In: Peterson, F.P. (eds) The Steenrod Algebra and Its Applications: A Conference to Celebrate N.E. Steenrod's Sixtieth Birthday. Lecture Notes in Mathematics, vol 168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058523

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  • DOI: https://doi.org/10.1007/BFb0058523

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05300-2

  • Online ISBN: 978-3-540-36437-5

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