Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model. We define the corresponding first-projection-simulation, and we prove some of its basic properties. With the Grothendieck computability model the category of computability models is shown to be a type-category, in the sense of Pitts, a result that bridges the categorical interpretation of dependent types with the theory of computability models. We introduce the notion of a fibration and opfibration-simulation, and we show that the first-projection-simulation is a split opfibration-simulation.
The Grothendieck Computability Model
Iosif Petrakis
2024-01-01
Abstract
Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model. We define the corresponding first-projection-simulation, and we prove some of its basic properties. With the Grothendieck computability model the category of computability models is shown to be a type-category, in the sense of Pitts, a result that bridges the categorical interpretation of dependent types with the theory of computability models. We introduce the notion of a fibration and opfibration-simulation, and we show that the first-projection-simulation is a split opfibration-simulation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.