Example 6.93.
A Kan fibration in any hypercomplete topos is a ``realization-fibration", i.e. pullback along a Kan fibration commutes with geometric realizations: if \(X_{\bullet} \to Z_{\bullet}\) is a Kan fibration and \(Y_{\bullet} \to Z_{\bullet}\) is arbitrary, we have
\[\colim_n X_n \times_{Z_n} Y_n \iso (\colim_n X_n) \times_{\colim_n Z_n} (\colim_n Y_n).\]