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

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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/}
}
TY  - JOUR
AU  - Peter Johnstone
TI  - A note on discrete Conduché fibrations
JO  - Theory and applications of categories
PY  - 1999
SP  - 1
EP  - 11
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_1999_5_a0/
LA  - en
ID  - TAC_1999_5_a0
ER  - 
%0 Journal Article
%A Peter Johnstone
%T A note on discrete Conduché fibrations
%J Theory and applications of categories
%D 1999
%P 1-11
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_1999_5_a0/
%G en
%F TAC_1999_5_a0
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/