Université catholique de Louvain

Institut de recherche en mathématique et physique

Bâtiment Marc de Hemptinne - Office 403

Chemin du Cyclotron, 2

1348 Louvain-la-Neuve

Belgium

Phone: +32 10 47 31 59

Email: pierre-alain *(dot)* jacqmin *(at)* uclouvain *(dot)* be

I am currently a FNRS postdoctoral researcher at the Université catholique de Louvain. I obtained my Ph.D. in 2016 at the Université catholique de Louvain under the supervision of Enrico Vitale and Zurab Janelidze. Between those two periods at UCLouvain, I was a postdoc and part-time professor at the University of Ottawa, working with Richard Blute, Thierry Giordano, Pieter Hofstra, Paul-Eugène Parent, Alistair Savage and Philip Scott. For more details, you can see my CV.

My research interests lie in Category Theory and everything connected to it, including Universal Algebra, Logic, Algebra and Categorical Algebra. More specifically, I work on the following themes and their interactions:

- pro-completion and ind-completion;
- locally presentable categories (also called essentially algebraic categories, or categories of partial algebras);
- (many sorted) algebraic categories;
- exactness properties;
- Mal'tsev categories, semi-abelian categories,...;
- embedding theorems (also called representation theorems);
- finiteness spaces and generalized convolution algebras;
- internal groupoids, fibrations and weak equivalences;
- (bi)category of fractions;
- homological lemmas;
- categorical Galois theory;
- ...

- [with M. Hoefnagel]: Matrix taxonomy and Bourn localization,
*to appear in Applied Categorical Structures*. - [with M. Hoefnagel and Z. Janelidze]: The matrix taxonomy of finitely complete categories,
*Theory and Applications of Categories***38 (19)**(2022), 737-790. - A class of exactness properties characterized via left Kan extensions,
*Journal of Pure and Applied Algebra***226 (1)**(2022), 106784. - [with Z. Janelidze]: On linear exactness properties,
*Journal of Algebra***583**(2021), 38-88. - [with Z. Janelidze]: On stability of exactness properties under the pro-completion,
*Advances in Mathematics***377**(2021), 107484. - [with D. Bourn and M. Gran]: On the naturalness of Mal'tsev categories, in Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics (eds. C. Casadio and P.J. Scott)
*Outstanding Contributions to Logic***20**(2021), 59-104. - [with J. Beauvais-Feisthauer, R. Blute, I. Dewan and B. Drummond]: Finiteness spaces, étale groupoids and their convolution algebras,
*Semigroup Forum***101 (2)**(2020), 243-258. - Embedding theorems for Janelidze's matrix conditions,
*Journal of Pure and Applied Algebra***224 (2)**(2020), 469-506. - Categories of weak fractions,
*Theory and Applications of Categories***34 (46)**(2019), 1526-1551. - Partial algebras and embedding theorems for (weakly) Mal'tsev categories and matrix conditions,
*Cahiers de Topologie et Géométrie Différentielle Catégoriques***60 (4)**(2019), 365-403. - [with S. Mantovani, G. Metere and E.M. Vitale]: Bipullbacks of fractions and the snail lemma,
*Journal of Pure and Applied Algebra***223 (12)**(2019), 5147-5162. - [with R. Blute, J.R.B. Cockett and P.J. Scott]: Finiteness spaces and generalized power series,
*Electronic Notes in Theoretical Computer Science***341**(2018), 5-22. - [with S. Mantovani, G. Metere and E.M. Vitale]: On fibrations between internal groupoids and their normalizations,
*Applied Categorical Structures***26 (5)**(2018), 1015-1039. - An embedding theorem for regular Mal'tsev categories,
*Journal of Pure and Applied Algebra***222 (5)**(2018), 1049-1068. - [with D. Rodelo]: Stability properties characterising
*n*-permutable categories,*Theory and Applications of Categories***32 (45)**(2017), 1563-1587. - [with E.M. Vitale]: Bicategories of fractions for groupoids in monadic categories,
*Tbilisi Mathematical Journal***8 (1)**(2015), 85-105.

- [with M. Hoefnagel]: When a matrix condition implies the Mal'tsev property,
*submitted for publication in Cahiers de Topologie et Géométrie Différentielle Catégoriques*. - [with M. Hoefnagel, Z. Janelidze and E. van der Walt]: On binary matrix properties,
*submitted for publication in Quaestiones Mathematicae*. - Surjection-like classes of morphisms,
*submitted for publication in Theory and Applications of Categories*.

- [with N. Egner and N. Martins-Ferreira]: Syntactical characterization of weakly Mal'tsev varieties.
- [with M. Hoefnagel]: A note on the atomicity of arithmeticity.
- [with M. Hoefnagel]: Partial algebras and implications of (weak) matrix properties.
- [with V. Aravantinos-Sotiropoulos and M. Hoefnagel]: Some exactness properties stable under the exact completion of a regular category.

- Ph.D. these at UCLouvain (2016): Embedding theorems in non-abelian categorical algebra (supervised by Enrico Vitale and Zurab Janelidze).
- Master these at UCLouvain (2013): Classification of cat-groups (supervised by Enrico Vitale).
- Part III essay at Cambridge (2012): Homology in semi-abelian categories (supervised by Julia Goedecke). A more detailed version can be found here.
- Undergraduate these at UCLouvain (2011): Sous-groupes normaux des groupes de matrices (supervised by Pierre-Emmanuel Caprace).

- [with M. Sebille]: EGMO 2017 à Zürich,
*Losanges***39**(2017), 54-59. - [with M. Sebille]: European Girl’s Mathematical Olympiad 2014 ou l’art de méjuger un questionnaire,
*Losanges***27**(2014), 60-64. - [with M. Sebille]: European Girl’s Mathematical Olympiad 2013,
*Losanges***21**(2013), 47-52. - [with M. Sebille]: European Girl’s Mathematical Olympiad 2012,
*Losanges***17**(2012), 50-55.

- Nadja Egner (since 2021), co-supervised also by Marino Gran (UCLouvain).
- Ineke van der Berg (since 2022), co-supervised also by Zurab Janelidze (University of Stellenbosch) and Alessandra Palmigiano (Vrije Universiteit Amsterdam).

- Spring 2022: Lecturer for Algèbre commutative (LMAT1331).
- Spring 2017: Teaching Assistant for Mathématiques Générales 1 (LMAT 1111 G).
- Spring 2015: Teaching Assistant for Mathématiques : algèbre et calcul matriciel (LINGE 1121).
- Autumn 2013: Teaching Assistant for Mathématiques Générales 1 (LMAT 1111 D).

- Fall 2018: Instructor for Méthodes Mathématiques II (MAT 1702 C).
- Winter 2018: Instructor for Mathematical Methods II (MAT 1302 B).
- Fall 2017: Instructor for Mathematical Methods I (MAT 1300 D).

From 2013, I am involved in the preparation of Belgian high school students for the International Mathematical Olympiad. I mostly teach general algebra and functional equations. I have been Deputy Leader of the Belgian team at the European Girl Mathematical Olympiad from 2012 to 2017 as well as Deputy Leader of the Belgian team at the Benelux Mathematical Olympiad from 2014 to 2016. I was also Leader of the Belgian team for the Olympiade Francophone de Mathématiques in 2020 and 2021.

- May 2022, Antwerp Algebra Colloquium, Antwerp, Belgium,
*An introduction to Mal'tsev categories*(invited talk). - April 2022, 5th Workshop on Categorical Algebra: Recent developments and future perspectives, Gargnano, Italy,
*Pro-completion, exactness properties and their implications*(invited talk). - April 2022, Junior Category Theory Seminar, Louvain-la-Neuve, Belgium,
*The Orthogonal Subcategory Problem*. - March 2022, Séminaire Sémantique de l'Institut de Recherche en Informatique Fondamentale, Paris, France,
*Propriétés d'exactitude stables par pro-complétion*(invited talk). - December 2021, Junior Category Theory Seminar, Louvain-la-Neuve, Belgium,
*Relations and their matrix properties*. - October 2021, Séminaire Itinérant de Catégories, Calais, France,
*Propriétés d’exactitude et leur caractérisation variétale*(invited talk). - August 2021, International Category Theory Conference (CT 20→21), Genoa, Italy,
*On classes of morphisms behaving like surjections*. - March 2021, Stellenbosch Seminar Series in Categorical Algebra, Stellenbosch, South Africa (online),
*On classes of morphisms behaving like surjections*. - March 2020, Junior Category Theory Seminar, Louvain-la-Neuve, Belgium,
*An introduction to Fraissé limits*. - January 2020, Departmental Colloquium, Stellenbosch, South Africa,
*Generalized rings of power series and finiteness spaces*(invited talk). - November 2019, Junior Category Theory Seminar, Louvain-la-Neuve, Belgium,
*Classical embedding theorems*. - June 2019, Ottawa-Carleton Logic Seminar, Ottawa, Canada,
*Weak reflections, polyfunctors and the small object argument*. - October 2018, Ottawa-Carleton Logic Seminar, Ottawa, Canada,
*Embedding theorem for (weakly) Mal'tsev categories*. - June 2018, 34th Conference on the Mathematical Foundations of Programming Semantics, Halifax, Canada,
*Finiteness spaces and generalized power series*. - May 2018, 4th Workshop on Categorical Algebra: Recent developments and future perspectives, Gargnano, Italy,
*Internal fibrations and their normalizations*(invited talk). - May 2018, UCL-ULB-VUB Category Theory Seminar, Louvain-la-Neuve, Belgium,
*Finiteness spaces and generalized power series*. - February 2018, Ottawa-Carleton Logic Seminar, Ottawa, Canada,
*Stability properties characterising n-permutable categories*. - February 2018, Ottawa-Carleton Logic Seminar, Ottawa, Canada,
*Functorial exactness properties*. - September 2017, Ottawa-Carleton Joint Algebra Seminar, Ottawa, Canada,
*Where the snake is just a snail*. - July 2017, International Category Theory Conference (CT 2017), Vancouver, Canada,
*An embedding theorem for regular Mal'tsev categories*. - May 2017, Category Theory Seminar, Cambridge, United Kingdom,
*Embedding theorems for (regular) Mal'tsev categories*(invited talk). - May 2016, 4th Workshop on Categorical Methods in Non-Abelian Algebra, Coimbra, Portugal,
*An embedding theorem for regular Mal'tsev categories*. - March 2016, UCL-ULB-VUB Category Theory Seminar, Brussels, Belgium,
*An embedding theorem for regular Mal'tsev categories*. - September 2015, Workshop in Category Theory and Algebraic Topology, Louvain-la-Neuve, Belgium,
*Bicategories of fractions for groupoids in monadic categories*. - January 2015, 97th Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve, Belgium,
*Exactness properties and cofiltered limit completion*. - November 2014, Brümmer 80 Seminar, Cape Town, South Africa,
*Embedding theorem for regular subtractive categories*. - October 2014, 57th South African Mathematical Society annual congress, Johannesburg, South Africa,
*Bicategories of fractions for groupoids in monadic categories*. - October 2014, Seminar of the Centre for Mathematical Structure, Stellenbosch, South Africa,
*An introduction to bicategories*.

Last update: 30 September 2022