A Unified Approach to Algebraic Set Theory

TL;DR

This paper introduces Algebraic Set Theory as a versatile categorical framework for analyzing various set theories, emphasizing applications to constructive set theories like IZF and CZF.

Contribution

It provides a comprehensive overview of AST, highlighting its flexibility and applications to different kinds of set theories, including constructive and classical ones.

Findings

AST offers a unifying categorical framework for set theories.

Application to constructive set theories IZF and CZF is emphasized.

Basic results and applications of AST are summarized.

Abstract

The paper provides an introduction to the field of Algebraic Set Theory (AST). AST is a flexible categorical framework for studying different kinds of set theories: both classical and constructive, predicative and impredicative. We discuss the basic results in this area, with a particular emphasis on applications to the constructive set theories IZF and CZF. (This paper is a summary of a tutorial on categorical logic given by the second named author at the Logic Colloquium 2006 in Nijmegen.)