  Let $\kappa$ be a regular cardinal. We study Gabriel-Ulmer duality when one
restricts the 2-category of locally $\kappa$-presentable categories with
$\kappa$-accessible right adjoints to its locally full sub-2-category of
$\kappa$-presentable Grothendieck topoi with geometric $\kappa$-accessible
morphisms. In particular, we provide a full understanding of the locally full
sub-2-category of the 2-category of $\kappa$-small cocomplete categories with
$\kappa$-colimit preserving functors arising as the corresponding 2-category of
presentations via the restriction. We analyse the relation of these
presentations of Grothendieck topoi with site presentations and we show that
the 2-category of locally $\kappa$-presentable Grothendieck topoi with
geometric $\kappa$-accessible morphisms is a reflective sub-bicategory of the
full sub-2-category of the 2-category of sites with morphisms of sites
genearated by the weakly $\kappa$-ary sites in the sense of Shulman [37].
