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Categorical interpolation: Descent and the Beck-Chevalley condition without direct images. (English) Zbl 0736.18005

Category theory, Proc. Int. Conf., Como/Italy 1990, Lect. Notes Math. 1488, 306-325 (1991).
[For the entire collection see Zbl 0733.00009.]
Fibred categories have been introduced by Grothendieck (1959, 1971) as the setting for his theory of descent. The present paper contains a characterization of the effective descent morphisms under an arbitrary fibred category. This essentially geometric result complements a logical analysis of the Beck-Chevalley property — which was crucial in the well-known theorem on sufficient conditions for the descent under bifibrations, due to Bénabou-Roubaud (1970) and Beck (unpublished). We describe the notion of interpolants as the common denominator of the concepts of descent and the Beck-Chevalley property.

MSC:

18D30 Fibered categories

Citations:

Zbl 0733.00009
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