## Research¶

Most of my research interest lies within the interaction of category theory and algebra, i.e., within *categorical algebra*. Generally speaking, I am interested in understanding various topics in algebra from the categorical point of view, as well as various topics in category theory from the algebraic point of view.

##### Publications¶

- 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.

##### Submitted for publication¶

- M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze.
*The matrix taxonomy of left exact categories*. Preprint available. - M. Hoefnagel.
*Anticommutativity and the traingular lemma*. arXiv:2008.00486 (2020).

##### Talks¶

*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*, 5^{th}Workshop in Categorical Methods in non-Abelian algebra, Lovain la Neuve, Belgium 2017.