A short proof of the localic groupoid representation of Grothendieck toposes

Christopher F. Townsend
2013 Proceedings of the American Mathematical Society  
It is known that each Grothendieck topos is the category of Gequivariant sheaves for some localic groupoid G. A simple proof of this is given which relies on the recently observed fact that the pullback adjunction between locales induced by any geometric morphism satisfies Frobenius reciprocity.
doi:10.1090/s0002-9939-2013-11829-0 fatcat:r7iqc56mgjg3nkt7wr3yrposyq