Geodesic
A note on discrete Conduché fibrations
Theory and applications of categories, Tome 5 (1999), pp. 1-11

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The class of functors known as discrete Conduché fibrations forms a common generalization of discrete fibrations and discrete opfibrations, and shares many of the formal properties of these two classes. F. Lamarche conjectured that, for any small category $\cal B$, the category ${\bf DCF}/{\cal B}$ of discrete Conduché fibrations over $\cal B$ should be a topos. In this note we show that, although for suitable categories $\cal B$ the discrete Conduché fibrations over $\cal B$ may be presented as the `sheaves' for a family of coverings on a category ${\cal B}_{tw}$ constructed from $\cal B$, they are in general very far from forming a topos.

Classification : Primary 18A22, Secondary 18B25.
Keywords: 
@article{TAC_1999_5_a0,
     author = {Peter Johnstone},
     title = {A note on discrete {Conduch\'e} fibrations},
     journal = {Theory and applications of categories},
     pages = {1--11},
     publisher = {mathdoc},
     volume = {5},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1999_5_a0/}
}
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Peter Johnstone. A note on discrete Conduché fibrations. Theory and applications of categories, Tome 5 (1999), pp. 1-11. http://geodesic.mathdoc.fr/item/TAC_1999_5_a0/