## 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¶

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

- 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.

##### Submitted for publication¶

- M. Hoefnagel, P.-A. Jacqmin, Z. Janelidze.
*The matrix taxonomy of left exact categories*(2021). - M. Hoefnagel, P.-A. Jacqmin.
*Matrix taxonomy and Bourn localization*(2021). - M. Hoefnagel, P.-A. Jacqmin,
*When a matrix condition implies the Mal'tsev property*(2021).

##### Talks¶

*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.