Matthieu Piquerez

A First Order Theory of Diagram Chasing

2023 · HAL (Le Centre pour la Communication Scientifique Directe)

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order …

Machine-Checked Categorical Diagrammatic Reasoning

2024 · arXiv (Cornell University)

This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language, which features dedicated …