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Abstract

Fibred categories were introduced by Gkothendieck in [SGA] and [BB190]. As far as I know these are the only easily available references to the subject. Through sheer luck, during the final preparation of this paper I obtained a copy of handwritten notes [BN] of a seminar given by Chevalley at Berkeley in 1962 which treated these questions from a slightly different point of view. We discuss the “Chevalley condition” in 3.11.

This work has been partially supported by the National Science Foundation under Grant No. gP-3624.

Received September 13, 1965.

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References

  1. Artin, M.: Grothendieck topologies. Seminar notes. Harvard University 1962.

    Google Scholar 

  2. Chevalley, C.: Categories and schemes (unpublished seminar notes). Berkeley: Univ. of Calif. 1962.

    Google Scholar 

  3. Giraud, J.: Analysis situs. Paris: Seminaire Bourbaki, n° 256, 1962-63.

    Google Scholar 

  4. Godement, R.: Topologie algébrique et théorie des faisceaux. Paris: Hermann 1958.

    MATH  Google Scholar 

  5. Gray, J. W.: Sheaves with values in a category. Topology 3,1–18 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Grothendieck, A.: Catégories fibrées et descente. Seminaire de géométrie algébrique de l’Institut des Hautes Études Scientifiques. Paris 1961.

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  7. — Technique de descente et théorèmes d’existence en géométrie algébrique, I. Généralités. Descente par morphismes fidélement Plats. Paris: Seminaire Bourbaki, n° 190, 1959–1960.

    Google Scholar 

  8. — avec J. Diendonné: Éléments de géométrie algébrique, I. Paris: Publ. Inst. Hautes Études Sci. No. 4, 1960.

    Google Scholar 

  9. Heller, A., and K. A. Rowe: On the category of sheaves. Amer. J. Math. 84, 205–216 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  10. Lawvere, F. William: Functorial semantics of algebraic theories. Thesis. New York: Columbia University 1963.

    Google Scholar 

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Gray, J.W. (1966). Fibred and Cofibred Categories. In: Eilenberg, S., Harrison, D.K., MacLane, S., Röhrl, H. (eds) Proceedings of the Conference on Categorical Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99902-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-99902-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-99904-8

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