## Research¶

My research focuses on several topics at the intersection of algebra and category theory.

##### Publications¶

Click on any of the papers below to be directed to corresponding paper.

- M. Hoefnagel,
*Centrality and the commutativity of finite products with coequalisers*, Theory and Applications of Categories 39 (13), 423-443, 2023. - M. Hoefnagel, P.-A. Jacqmin.
*Matrix taxonomy and Bourn localization*, Applied Categorical Structures, 2022. - M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze.
*The matrix taxonomy of finitely complete categories*. Theory and Applications of Categories 38,737-790, 2022. - M. Hoefnagel.
*Anticommutativity and the triangular lemma*. Algebra Universalis 82 (19), 2021. - M. Hoefnagel, D. Rodelo and Z. Janelidze.
*On difunctionality of class relations*. Algebra Universalis 81 (19), 2020. - M. Hoefnagel.
*M-coextensive objects and the strict refinement property*. Journal of Pure and Applied Algebra 224 (10), 2020. - M. Hoefnagel.
*Characterizations of majority categories*. Applied Categorical Structures 28, 113–134, 2020. - M. Hoefnagel.
*Products and coequalizers in pointed categories*. Theory and Applications of Categories 34, 1386–1400, 2019. - M. Hoefnagel.
*Majority categories*. Theory and Applications of Categories 34, 249–268, 2019. - M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze, E. van der Walt.
*On binary matrix properties*, Quaestiones Mathematicae, 2023.

##### Submitted for publication¶

- M. Hoefnagel, P.-A. Jacqmin,
*When a matrix condition implies the Mal'tsev property*, arXiv:2208.09516. - M. Hoefnagel, P.-A. Jacqmin,
*A note on the atomicity of arithmeticity*, arXiv:2401.06414. - M. Hoefnagel, D. Rodelo,
*Categorical aspects of congruence distributivity*, arXiv:2401.05325.

##### In preparation¶

- M. Hoefnagel,
*A characterisation of the commutativity of finite products with coequalisers in general varieties of algebras*, preprint available. - M. Hoefnagel, D. Rodelo,
*Mitschke's theorem in regular categories*. - M. Hoefnagel, E. Theart,
*On extensivity of morphisms in general categories*.

##### Talks / Posters¶

Click on the text below for the slides.

*On the commutativity of binary products and coequalisers*, International Conference in Category Theory (CT2023), 2023.*Matrix taxonomy of finitely complete categories*, Annual congress of the South African Mathematics Society, 2022.*On the commutativity of binary products and coequalisers*, Annual congress of the South African Mathematics Society, 2022.*Matrix taxonomy*, Category Theory Seminar at UCLouvain, 2022.*Deciding implications of matrix properties*, Centre for mathematics, University of Coimbra, 2021.*A classification of left exact (finitely complete) categories (motivated from universal algebra)*, Panglobal Algebra and Logic Seminar, 2020.*Coextensivity and the strict refinement property*, Annual congress of the South African Mathematics Society, 2019.*From the commutativity of products and coequalizers to Gumm's shifting lemma*, Categorical structures in Algebra, Topology and Logic, Stellenbosch University, 2019.*M-coextensivity and the strict refinement property*, Talk given at CT2019 the international conference in category theory, Edinburgh, 2019.*A Krull-Schmidt type theorem for direct decompositions in majority categories*, Annual congress of the South African Mathematics Society, Potchefstroom 2017.*Majority categories*, 5th Workshop in Categorical Methods in non-Abelian algebra, Lovain la Neuve, Belgium 2017.