#
A note on discrete Conduché fibrations

##
Peter Johnstone

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.

Keywords:

1991 MSC: Primary 18A22, Secondary 18B25.

*Theory and Applications of Categories*, Vol. 5, 1999, No. 1, pp 1-11.

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