Definition 6.52.
Let \(n \geq -1\). A topos \(T\) is called \(n\)-localic if for every topos \(S\) the induced functor
\[\Geom(S,T) \longrightarrow \Geom(S_{\leq n-1}, T_{\leq n-1}) := \Fun^{\lex, \colim}(T_{\leq n-1}, S_{\leq n-1})\]
is an equivalence.