Categories of assemblies for realizability

TL;DR

This paper introduces categories of assemblies related to realizability interpretations, based on a key subcategory of the effective topos, and characterizes these categories with specific properties.

Contribution

It presents a new framework for categories of assemblies linked to realizability, expanding understanding of their structure and properties.

Findings

Characterization of categories of assemblies by specific properties

Connection established between assemblies and the effective topos

Framework aids in understanding realizability interpretations

Abstract

This paper introduces categories of assemblies which are closely connected to realizability interpretations and which are based on an important subcategory of the effective topos. There is a list of properties which characterize these categories of assemblies up to equivalence.