The Gödel Fibration

We introduce the notion of a Gödel fibration, which is a fibration categorically embodying both the logical principles 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 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 Gödel fibration. This result establishes an intrinsic presentation of the Dialectica fibration, contributing to the understanding of the Dialectica construction itself and of its properties from a logical perspective.