Reference Artin glueing [wraith-artin-glueing-1974]

The source for Artin gluing at topos level: for a finite-limit-preserving functor F : \cE \to \cS between (elementary) toposes, the comma category \cS \downarrow F — objects are triples (s, e, f : s \to F e) — is again a topos. The construction abstracts the recollement of a topos of sheaves from an open subspace and its closed complement (SGA4); \cE sits inside the gluing as an open subtopos and \cS as its closed complement. See Carboni–Johnstone for the sharpest hypotheses on F, and the Elephant (Johnstone, A2.1.12, A4.5.6) for the textbook treatment.

@article{wraith-artin-glueing-1974, title={Artin glueing}, journal={Journal of Pure and Applied Algebra}, volume={4}, number={3}, pages={345--348}, author={Wraith, Gavin C.}, year={1974}}