Reference Connected limits, familial representability and Artin glueing [carboni-johnstone-artin-glueing-1995]

Sharpens Wraith's theorem: the gluing \cS \downarrow F along a functor F : \cE \to \cS between toposes is a topos iff F preserves pullbacks (preservation of the terminal object is not needed), and this is related to familial representability and preservation of connected limits. A corrigendum (same journal, 2004) repairs one of the auxiliary characterizations; the gluing theorem itself stands.

@article{carboni-johnstone-artin-glueing-1995, title={Connected limits, familial representability and Artin glueing}, journal={Mathematical Structures in Computer Science}, volume={5}, number={4}, pages={441--459}, author={Carboni, Aurelio and Johnstone, Peter T.}, year={1995}}