On the correspondence between gerbes and bouquets

Abstract

Duskin [1, 2] showed that gerbes over a Grothendieck toposEcan be interpreted by certain internal groupoids ofEwhich he called bouquets. He proved that for any bouquetBofEthe fibred category Fors(B) ofB-torsors is a gerbe overE, and conversely that any gerbe G gives rise to a bouquetBsatisfying G ≅ F ors(B). We want to give here a somewhat different approach to these results, based on a construction of gerbes given in [3].