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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Artin, M.: Grothendieck topologies. Seminar notes. Harvard University 1962.
Chevalley, C.: Categories and schemes (unpublished seminar notes). Berkeley: Univ. of Calif. 1962.
Giraud, J.: Analysis situs. Paris: Seminaire Bourbaki, n° 256, 1962-63.
Godement, R.: Topologie algébrique et théorie des faisceaux. Paris: Hermann 1958.
Gray, J. W.: Sheaves with values in a category. Topology 3,1–18 (1965)
Grothendieck, A.: Catégories fibrées et descente. Seminaire de géométrie algébrique de l’Institut des Hautes Études Scientifiques. Paris 1961.
— Technique de descente et théorèmes d’existence en géométrie algébrique, I. Généralités. Descente par morphismes fidélement Plats. Paris: Seminaire Bourbaki, n° 190, 1959–1960.
— avec J. Diendonné: Éléments de géométrie algébrique, I. Paris: Publ. Inst. Hautes Études Sci. No. 4, 1960.
Heller, A., and K. A. Rowe: On the category of sheaves. Amer. J. Math. 84, 205–216 (1962).
Lawvere, F. William: Functorial semantics of algebraic theories. Thesis. New York: Columbia University 1963.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1966 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-99902-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-99904-8
Online ISBN: 978-3-642-99902-4
eBook Packages: Springer Book Archive