An Introduction to Categorical Proof Theory

TL;DR

This paper provides an accessible introduction to categorical proof theory, explaining how categorical methods can be applied to proof theory with minimal prerequisites and emphasizing philosophical aspects.

Contribution

It offers a beginner-friendly overview of categorical proof theory, integrating applications and foundational concepts without requiring prior category theory knowledge.

Findings

Introduces categorical proof theory concepts clearly for newcomers

Highlights applications of categorical methods in proof theory

Bridges philosophical and formal aspects of proofs

Abstract

These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various applications of categorical methods in proof theory. It is designed to be accessible, with no prior familiarity with category theory required. The necessary categorical background is introduced gradually, with a focus on the philosophical and informal aspects of proof. The only prerequisites are a basic understanding of logic, computability theory, topology, and ordered structures.