Research

My research explores several themes at the intersection of algebra and category theory, with particular interest in , coextensivity and its relationship to refinement and unique factorisation, cetrality and its relation to commutativity of finite products with coequalisers, exactness properties in categorical algebra, semi-abelian properties of Heyting semi-lattices, arithmetical and majority categories (and related notions).

Publications

Click on any of the entries below to view the corresponding article.

  1. Majority categories, Theory and Applications of Categories, Vol. 34, 249–268, 2019.
  2. Products and coequalizers in pointed categories, Theory and Applications of Categories, Vol. 34, 1386–1400, 2019.
  3. Characterizations of majority categories, Applied Categorical Structures, 28, 113–134, 2020.
  4. M-coextensive objects and the strict refinement property, Journal of Pure and Applied Algebra, 224 (10), 2020.
  5. (with D. Rodelo and Z. Janelidze) On difunctionality of class relations, Algebra Universalis, 81 (19), 2020.
  6. Anticommutativity and the triangular lemma, Algebra Universalis, 82 (19), 2021.
  7. (with P.-A. Jacqmin, Z. Janelidze) The matrix taxonomy of finitely complete categories, Theory and Applications of Categories, Vol. 38, 737–790, 2022.
  8. (with P.-A. Jacqmin) Matrix taxonomy and Bourn localization, Applied Categorical Structures, 2022.
  9. Centrality and the commutativity of finite products with coequalisers, Theory and Applications of Categories, Vol. 39 (13), 423–443, 2023.
  10. (with P.-A. Jacqmin, Z. Janelidze, E. van der Walt) On binary matrix properties, Quaestiones Mathematicae, 2023.
  11. (with D. Rodelo) Categorical aspects of congruence distributivity, Theory and Applications of Categories, Vol. 41, 2024, No. 17, pp 531–550.
  12. (with D. Bourn) On n-unital and n-Mal’tsev categories, Applied Categorical Structures, 32, 32, 2024.
  13. (with P.-A. Jacqmin) Partial Algebras and Implications of (Weak) Matrix Properties, Applied Categorical Structures, 32, 34, 2024.
  14. (with E. Theart) On extensivity and coextensivity of morphisms, Theory and Applications of Categories, Vol. 44, 2025, No. 21, pp 617–642.
  15. (with P.-A. Jacqmin) When a matrix condition implies the Mal’tsev property, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume LXVI (2025), No. 3, pp. 32–64.
  16. (with P.-A. Jacqmin)A note on the atomicity of arithmeticity, Theory and Applications of Categories, Vol. 44, No. 23, 2025, pp. 664–675.
  17. (with X. García-Martínez, J. R. A. Gray, M. A. Hoefnagel, T. Van der Linden & C. Vienne)Categorical-algebraic aspects of Heyting semilattices, 2025. arXiv:2508.11250
  18. (with Z. Janelidze)Abelian objects in categories with normal projections, Theory anf Applications of Categories, 2025 (accepted)

Submitted for Publication

In Preparation

  • (with J.R.A Gray) Normality in finitely complete categories, in preparation
  • (with X. García-Martínez, J. R. A. Gray, M. A. Hoefnagel, T. Van der Linden & C. Vienne) Algebraic coherence in the variety of Heyting semilattices, in preparation.
  • A characterisation of the commutativity of finite products with coequalisers in general varieties of algebras, preprint available.
  • (with D. Rodelo) Mitschke's theorem in regular categories
  • (with R. Ferguson and E. Theart) Functorial approximations of coproducts, in preparation.
  • (with Z. Janelidze) Nullital categories, in preparation.