  We introduce the notion of a G\"odel fibration, which is a fibration
categorically embodying both the logical principle of traditional Skolemization
(we can exchange the order of quantifiers paying the price of a functional) and
the existence of a prenex normal form presentation for every logical formula.
Building up from Hofstra's earlier fibrational characterization of the de
Paiva's categorical Dialectica construction, we show that a fibration is an
instance of the Dialectica construction if and only if it is a G\"odel
fibration. This result establishes an internal presentation of the dialectica
construction. Then we provide a deep structural analysis of the Dialectica
construction producing a full description of which categorical structure
behaves well with respect to this construction, focusing on (weak) finite
products and coproducts. We conclude describing the applications we envisage
for this generalized fibrational version of the Dialectica construction.
