Recent talks

Colloquium talk on "Categories, groups and non-abelian algebraic structures'' at NITheCS, Stellenbosch (March 2023)
Invited talk on ``Some new examples of pretorsion theories'' at the "Conference Categories, Rings and Modules", Accademia Galileiana, Padova (January 2023)
Invited talk on ``Pretorsion theories'' at the International Category Theory Conference 2021, Genova (August 2021)

Publications

2024

Pretorsion theories in lextensive categories (with F. Borceux and F. Campanini) accepted in Israel Journal of Mathematics, 2024.
Conditional flatness, fiberwise localizations, and admissible reflections (with J. Scherer), Journal of the Australian Mathematical Society, 116 (2), 200-220, 2024.
Ideals and Congruences in L-algebras and Pre-L-algebras (with A. Facchini and M. Pompili), Categories and General Algebraic Structures with Applications, 2024.
Hopf formulae for homology of skew braces (with T. Letourmy and L. Vendramin), preprint, 2024.
Double groupoids and 2-groupoids in regular Mal'tsev categories (with N. Egner), preprint, 2024.

2023

Central extensions of preordered groups (with A. Michel), Bulletin de la Société Mathématique de France, 151 (4), 659-686, 2023.
Groupoids and skeletal categories form a pretorsion theory in Cat (with F. Borceux, F. Campanini and W. Tholen), Advances in Mathematics, 426, 109110, 2023.

2022

The stable category of preorders in a pretopos I: General theory (with F. Borceux and F. Campanini), Journal of Pure and Applied Algebra, 2022, 106997.
The stable category of preorders in a pretopos II: the universal property (with F. Borceux and F. Campanini), Annali di Matematica Pura e Applicata, 201, 2847-2869, 2022.

2021

An introduction to regular categories, in New perspectives in Algebra, Topology and Categories Coimbra Mathematical Texts, Vol. 1, Eds. M.M. Clementino, A. Facchini and M. Gran, Springer, 113-145, 2021.
Action representability of the category of internal groupoids (with J. R. Gray) Theory and Applications of Categories, Vol. 37 (1) 2021, 1-13.
Torsion theories and coverings of preordered groups (with A. Michel), Algebra Universalis, 82, 22, 2021.
On the naturalness of Mal'tsev categories (with D. Bourn and P.-A. Jacqmin), Joachim Lambek: the interplay of Mathematics, Logic and Linguistics Outstanding Contributions to Logic, Vol. 20, Eds. C. Casadio and P. Scott, Springer, 59-104, 2021.
Pretorsion theories in general categories (with A. Facchini and C. Finocchiaro), Journal of Pure and Applied Algebra, Vol. 225, 2021, 106503.

2020

Unusual spectral categories (with M.J. Arroyo Paniagua, A. Facchini and G. Janelidze), Rendiconti del Seminario Matematico dell'Università di Padova, Vol.144, 2020, 13-25.
A new Galois structure in the category of internal preorders (with A. Facchini and C. Finocchiaro), Theory and Applications of Categories, Vol. 35 (11) 2020, 326-349.
What is the spectral category? (with M.J. Arroyo Paniagua, A. Facchini and G. Janelidze), Advances in Rings, Modules and Factorizations, Springer Proceedings in Mathematics and Statistics, Vol. 321, 2020, 135-152.
Facets of congruence distributivity in Goursat categories (with D. Rodelo and I. Tchoffo Nguefeu), Journal of Pure and Applied Algebra, 224 (10), 2020, 106380.
Galois theory and the categorical Peiffer commutator (with A.S. Cigoli, A. Duvieusart and S. Mantovani), Homology, Homotopy and Applications, 22 (2) 2020, 323-346
Monoidal characterisation of groupoids and connectors (with C. Heunen and S. Tull), Topology and Its Applications, Vol. 273, 2020, 106966.

2019

Split extensions and semidirect products of unitary magmas (with G. Janelidze and M. Sobral), Comment. Math. Univ. Carolin., 60 (4) 2019, 509-527.
A semi-abelian extension of a theorem by Takeuchi (with F. Sterck and J. Vercruysse), Journal of Pure and Applied Algebra, Vol. 223 (10) 2019, 4171-4190.
Variations of the Shifting Lemma and Goursat categories (with D. Rodelo and I. Tchoffo Nguefeu), Algebra Universalis, Vol. 80:2, 2019, 1-12.

2018

A relative monotone-light factorisation system for internal groupoids (with A. Cigoli and T. Everaert), Applied Categorical Structures, Vol. 26 (5) 2018, 931-942.
Some remarks on protolocalisations and protoadditive reflections (with M.M. Clementino and G. Janelidze), Journal of Algebra and Its Applications, Vol. 17 (11), 2018, 1850207, 16 pp.
Higher commutator conditions for extensions in Mal'tsev categories (with A. Duvieusart), Journal of Algebra, 515, 2018, 298-327.
Split extension classifiers in the category of cocommutative Hopf algebras (with G. Kadjo and J. Vercruysse), Bulletin of the Belgian Mathematical Society S. Stevin, Vol. 25, No. 3, 2018, 355-382.

2017

Some remarks on connectors and groupoids in Goursat categories (with D. Rodelo and I. Tchoffo Nguefeu), Logical Methods in Computer Science, Vol. 13, No. 3, 2017, 1-12.
Epireflective subcategories and formal closure operators (with M. Duckerts-Antoine and Z. Janelidze), Theory and Applications of Categories, Vol. 32, No. 15, 2017, 526-546.
Beck-Chevalley condition and Goursat categories (with D. Rodelo), Journal of Pure and Applied Algebra, Vol. 221, No. 10, 2017, 2445-2457.

2016

Semi-localizations of semi-abelian categories (with S. Lack), Journal of Algebra, Vol. 454, 2016, 206-232.
Closure operators in the category of quandles (with V. Even), Topology and its Applications, Vol. 200, No. 1, 2016, 237-250.
A characterization of central extensions in the variety of quandles (with V. Even and A. Montoli), Theory and Applications of Categories, Vol. 31, No. 8, 2016, 201-216.
A torsion theory in the category of cocommutative Hopf algebras (with G. Kadjo and J. Vercruysse), Applied Categorical Structures, Vol. 24, No. 3, 2016, 269-282.

2015

Some aspects of semi-abelian homology and protoadditive functors (with T. Everaert), Journal of Generalized Lie Theory and Applications, Vol. 9:238, 2015, 1000238.
Protoadditive functors, derived torsion theories and homology (with T. Everaert), Journal of Pure and Applied Algebra, 219, No. 8, 2015, 3629-3676.

2014

Some remarks on pullbacks in Gumm categories (with D. Rodelo), Texts on Mathematics, Vol. 46, University of Coimbra, 2014, 125-136.
Weighted commutators in semi-abelian categories (with G. Janelidze and A. Ursini), Journal of Algebra, 397, 2014, 643-665.
On factorization systems for surjective quandle homomorphisms (with V. Even), Journal of Knot Theory and Its Ramifications, Vol. 23, No. 11, 2014, 1450060.
The Cuboid Lemma and Mal'tsev categories (with D. Rodelo), Applied Categorical Structures, Vol. 22, 2014, 805-816.
On 2-star-permutability in regular multi-pointed categories (with D. Rodelo), Journal of Algebra and its Applications, Vol. 13, No. 8, 2014, 1450068.
Star-regularity and regular completions (with Z. Janelidze), Journal of Pure and Applied Algebra, 218, No. 2, 2014, 1771-1782.

2013

Effective descent morphisms in star-regular categories (with O. Ngaha), Homology, Homotopy and Applications, Vol. 15, No 2, 2013, 127-144.
Monotone-light factorisation systems and torsion theories (with T. Everaert), Bulletin des Sciences Mathématiques, 137, 2013, 996-1006.

2012

Symmetry of regular diamonds, the Goursat property, and subtractivity (with Z. Janelidze, D. Rodelo and A. Ursini), Theory and Applications of Categories, Vol. 27, No. 6, 2012, 80-96.
On the characterisation of Jónsson-Tarski and of subtractive varieties (with D. Rodelo), Diagrammes, Suppl. Vol. 67-68, 2012, 101-116.
3 x 3 lemma for star-exact sequences (with Z. Janelidze and D. Rodelo), Homology, Homotopy and Applications, Vol. 14, No 2, 2012, 1-22.
A New Characterisation of Goursat Categories (with D. Rodelo), Applied Categorical Structures, Vol. 20, No 3, 2012, 229-238.
A description of the fundamental group in terms of commutators and closure operators (with M. Duckerts and T. Everaert), Journal of Pure and Applied Algebra, Vol. 216, 2012, 1837-1851.
A good theory of ideals in regular multi-pointed categories (with Z. Janelidze and A. Ursini), Journal of Pure and Applied Algebra, Vol. 216, 2012, 1905-1919.

2010

Homology of n-fold groupoids (with T. Everaert), Theory and Applications of Categories, Vol. 23, No. 2, 2010, 22-41.

2009

Covering morphisms and normal extensions in Galois structures associated with torsion theories (with G. Janelidze), Cahiers de Topologie et Géométrie Différentielle Catégoriques, L-3, 2009, 171-188.

2008

Higher Hopf formulae for homology via Galois theory (with T. Everaert and T. Van der Linden), Advances in Mathematics, Vol. 217, 2008, 2231-2267.
On the second cohomology group in semi-abelian categories (with T. Van der Linden), Journal of Pure and Applied Algebra, Vol. 212, 2008, 636-651.
Protolocalisations of homological categories (with F. Borceux, M.M. Clementino and L. Sousa), Journal of Pure and Applied Algebra, Vol. 212, 2008, 1898-1927.
Protolocalisations of exact Mal'cev categories (with F. Borceux et S. Mantovani), Theory and Applications of Categories, Vol. 21, No. 3, 2008, 37-60.
A universal construction in Goursat categories (with D. Rodelo), Cahiers de Topologie et Géométrie Différentielle Catégoriques, XVIX-3, 2008, 196-208.

2007

On low-dimensional homology in categories (with T. Everaert), Homology, Homotopy and Applications, Vol. 9, No. 1, 2007, 275-293.
On closure operators and reflections in Goursat categories (with F. Borceux and S. Mantovani), Rendiconti dell'Istituto Matematico di Trieste, Vol. 39, 2007, 87-104.
Torsion theories and Galois coverings of topological groups (with V. Rossi), Journal of Pure and Applied Algebra, 208, 2007, 135-151.

2006

Relative commutator associated with varieties of n-nilpotent and of n-solvable groups (with T. Everaert), Archivum Mathematicum, Vol. 42, No. 4, 2006, 387-396.
Torsion theories in homological categories (with D. Bourn), Journal of Algebra, 305, 2006, 18-47.
Precrossed modules and Galois Theory (with T. Everaert), Journal of Algebra, 297, 2006, 292-309.

2004

Galois Theory and Double Central Extensions (with V. Rossi), Homology, Homotopy and Applications, Vol. 6, No. 1, 2004, 283-298.
Special reflexive graphs in modular varieties (with J. Rosický), Algebra Universalis, 52, 2004, 89-102.
Semi-abelian monadic categories (with J. Rosický), Theory and Applications of Categories, Vol. 13, No. 6, 2004, 106-113.
Applications of Categorical Galois Theory in Universal Algebra, in "Galois Theory, Hopf Algebras and Semiabelian Categories", The Fields Institute Communications Series, Vol. 43, 2004, 243-280.
Categorical aspects of modularity (with D. Bourn), in "Galois Theory, Hopf Algebras and Semiabelian Categories", The Fields Institute Communications Series, Vol. 43, 2004, 77-100.
Normal sections and direct product decompositions (with D. Bourn), Communications in Algebra, Vol. 32, No. 10, 2004, 3825-3842.
Regular, Protomodular and Abelian Categories (with D. Bourn), in Categorical Foundations - Special Topics in Order, Topology, Algebra and Sheaf Theory, Eds. M.C. Pedicchio and W. Tholen, Cambridge University Press, Encyclopedia of Mathematics and its Applications 97, 2004, 165-211.

2002

Centrality and connectors in Maltsev categories (with D. Bourn), Algebra Universalis, 48 (3), 2002, 309-331.
Semi-abelian exact completions, Homology, Homotopy and Applications, Vol. 4 (1), 2002, 175-189.
Central extensions in semi-abelian categories, (with D. Bourn), Journal of Pure and Applied Algebra, 175, 2002, 31-44.
Commutators and central extensions in universal algebra, Journal of Pure and Applied Algebra, 174, 2002, 249-261.
Centrality and normality in protomodular categories, (with D. Bourn), Theory and Applications of Categories, Vol. 9, No. 8, 2002, 151-165.

2001

n-permutable locally finitely presentable categories, (with M.C. Pedicchio), Theory and Applications of Categories , Vol. 8, No. 1, 2001, 1-15.
Central extensions and internal groupoids in Maltsev categories, Journal of Pure and Applied Algebra, 155, 2001, 139-166.

1999

Localizations of Maltsev varieties, (with E. Vitale), Theory and Applications of Categories, Vol. 5, No. 12, 1999, 281-291.
Internal categories in Mal´cev categories, Journal of Pure and Applied Algebra, 143, 1999, 221-229.

1998

On the exact completion of the homotopy category, (with E. Vitale), Cahiers de Topologie et Géométrie Différentielle Catégoriques, XXXIX-4, 1998, 287-297.