A First Order Theory of Diagram Chasing

Authors Assia Mahboubi , Matthieu Piquerez

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Author Details

Assia Mahboubi
  • Nantes Université, École Centrale Nantes, CNRS, INRIA, LS2N, UMR 6004, France
  • Vrije Universiteit Amsterdam, The Netherlands
Matthieu Piquerez
  • Nantes Université, École Centrale Nantes, CNRS, INRIA, LS2N, UMR 6004, France


The authors would like to thank Kenji Maillard, Loïc Pujet and the anonymous reviewers for their useful comments and suggestions on this work.

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Assia Mahboubi and Matthieu Piquerez. A First Order Theory of Diagram Chasing. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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 theory, and we study the models and decidability of this theory. The longer-term motivation of this work is the design of a computer-aided instrument for writing reliable proofs in homological algebra, based on interactive theorem provers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Diagram chasing
  • formal proofs
  • abelian categories
  • decidability


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