Definition 6.67.
Let \(\phi_*\colon S \to T\) be a morphism of topoi. We say that \(\phi_*\) has dimension \(\leq d\) if, for every \(n \geq d-1\), the functor \(\phi_*\) sends \(n\)-connected maps to \((n-d)\)-connected maps.
We say that \(T\) has dimension \(\leq d\) if the terminal morphism \(\Gamma_* = \Hom_T(*,-)\colon T \to \An\) has dimension \(\leq d\).