Tim Van der Linden

Maître de recherches of the Fonds de la Recherche Scientifique–FNRS,
attached to the Université catholique de Louvain
and partly to the Vrije Universiteit Brussel.

In Louvain

Office b.420, in the Marc de Hemptinne building;   phone +32 10 473179

In Brussels

Office G.6.07

Email

tim.vanderlinden@uclouvain.be   and   tim.van.der.linden@vub.be

Enseignement à l'UCLouvain

Je suis le président du jury du bachelier et des masters en sciences mathématiques.

Premier quadrimestre 2024–25 : le cours LMAT2215 - Homological Algebra.

Deuxième quadrimestre 2023–24 : le cours LMAT1235 - Notions de logique mathématique.

Research

Keywords

categorical algebra; categorical Galois theory; (co)homology of non-abelian algebraic structures; commutator theory, central extensions; homotopical algebra, Quillen model structures

Editorial work

I am an editor of the journal Theory and Applications of Categories.

I am a managing editor of Advanced Studies: Euro-Tbilisi Mathematical Journal.

Seminar

I co-organise the Category Theory Seminar which alternates between UCLouvain, ULB and VUB.

Work-in-progress

A Homological View of Categorical Algebra
With George Peschke; preprint arXiv:2404.15896.

Higher extensions in exact Mal'tsev categories: distributivity of congruences and the 3ⁿ-Lemma
With Cyrille Sandry Simeu; preprint arXiv:1807.03164.

Articles submitted for publication

The cohomology objects of a semi-abelian variety are small
With Sébastien Mattenet and Raphaël Jungers; preprint arXiv:2411.17200.

A comparison between weakly protomodular and protomodular objects in unital categories
With Xabier García-Martínez, Andrea Montoli and Diana Rodelo; preprint Pré-Publicações DMUC 24-41 (2024), 1–8.

Non-additive derived functors via chain resolutions
With Maxime Culot and Fara Renaud; preprint arXiv:2406.13398.

Weak representability of actions of non-associative algebras
With Jose Brox, Xabier García-Martínez, Manuel Mancini and Corentin Vienne; preprint arXiv:2306.02812.

Duality in non-abelian algebra V. Homological diagram lemmas
With Kishan Kumar Dayaram, Amartya Goswami and Zurab Janelidze; preprint arXiv:2303.11769.

Published articles

A universal Kaluzhnin–Krasner embedding theorem, Proc. Amer. Math. Soc. 152 (2024), no. 12, 5039–5053.
With Bo Shan Deval and Xabier García-Martínez; preprint arXiv:2306.15458.

Twisted Commutators and Internal Crossed Modules, Adv. Stu. Euro-Tbil. Math. J. 17 (2024), no. 3, 25–52.
With Bo Shan Deval; preprint arXiv:2311.07489.

Schur- and Baer-type theorems for Lie and Leibniz algebras, Bull. Belg. Math. Soc. Simon Stevin 30 (2023), issue 3, 386–398.
With Guram Donadze; preprint arXiv:2306.05794.

Associativity and the cosmash product in operadic varieties of algebras, Illinois J. Math. 67 (2023), issue 3, 563–598.
With Ülo Reimaa and Corentin Vienne; preprint arXiv:2206.12096.

A symmetric approach to higher coverings in categorical Galois theory, Appl. Categ. Structures 31 (2023), no. 10.
With Fara Renaud; preprint arXiv:2206.00949.

Algebraic logoi, J. Pure Appl. Algebra 227 (2023), 107293.
With Dominique Bourn, Alan S. Cigoli and James R. A. Gray; preprint arXiv:2112.08829.

Algebras with representable representations, Proc. Edinb. Math. Soc. (2) 64 (2021), 555–573.
With Xabier García-Martínez, Matsvei Tsishyn and Corentin Vienne.

Non-associative algebras, New Perspectives in Algebra, Topology and Categories (M. M. Clementino, A. Facchini and M. Gran, eds.), Coimbra Mathematical Texts, vol. 1, Springer, Cham, 2021, pp. 225–258.
Preprint arXiv:2004.06392.

Intrinsic Schreier special objects, Theory Appl. Categ. 36 (2021), no. 18, 514–555.
With Andrea Montoli and Diana Rodelo.

On the ternary commutator, I: Exact Mal'tsev categories, Theory Appl. Categ. 36 (2021), no. 15, 379–422.
With Cyrille Sandry Simeu.

Universal central extensions of internal crossed modules via the non-abelian tensor product, Appl. Categ. Structures 28 (2020), 717–748.
With Davide di Micco; preprint arXiv:2001.02874.

An intrinsic approach to the non-abelian tensor product via internal crossed squares, Theory Appl. Categ. 35 (2020), no. 34, 1268–1311.
With Davide di Micco.

Compatible actions in semi-abelian categories, Homology, Homotopy and Appl. 22 (2020), 221–250.
With Davide di Micco; preprint arXiv:1908.04184.

Intrinsic Schreier split extensions, Appl. Categ. Structures 28 (2020), 517–538.
With Andrea Montoli and Diana Rodelo; preprint arXiv:1911.08770.

On the “Three Subobjects Lemma” and its higher-order generalisations, J. Algebra 546 (2020), 315–340.
With Cyrille Sandry Simeu; preprint arXiv:1904.00161.

A comonadic interpretation of Baues-Ellis homology of crossed modules, J. Homotopy Relat. Struct. 14 (2019), 625–646.
With Guram Donadze; preprint arXiv:1805.07748.

A characterisation of Lie algebras amongst anti-commutative algebras, J. Pure Appl. Algebra 223 (2019), 4857–4870.
With Xabier García-Martínez; preprint arXiv:1701.05493.

A characterisation of Lie algebras via algebraic exponentiation, Adv. Math. 341 (2019), 92–117.
With Xabier García-Martínez; preprint arXiv:1711.00689.

A note on split extensions of bialgebras, Forum Math. 30 (2018), No. 5, 1089–1096.
With Xabier García-Martínez; preprint arXiv:1701.00665.

A Seifert–van Kampen theorem in non-abelian algebra, Homology, Homotopy and Appl. 20 (2018), No. 2, 79–103.
With Mathieu Duckerts-Antoine; preprint Pré-Publicações DMUC 16-45 (2016), 1–28.

Two characterisations of groups amongst monoids, J. Pure Appl. Algebra 222 (2018), No. 4, 747–777.
With Andrea Montoli and Diana Rodelo; preprint arXiv:1606.08649.

Do n-Lie algebras have universal enveloping algebras? J. Lie Theory 28 (2018), No. 1, 043–055.
With Xabier García-Martínez and Rustam Turdibaev; preprint arXiv:1508.06940.

What is an ideal a zero-class of? J. Algebra Appl. 16 (2017), no. 3, 1750049 (16 pages).
With Nelson Martins-Ferreira, Andrea Montoli and Aldo Ursini; preprint arXiv:1602.08627.

A criterion for reflectiveness of normal extensions, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 5, 667–692.
With Andrea Montoli and Diana Rodelo; preprint arXiv:1602.02515.

Higher central extensions and cohomology, Adv. Math. 287 (2016), 31–108.
With Diana Rodelo; preprint arXiv:1502.05282.

The Yoneda isomorphism commutes with homology, J. Pure Appl. Algebra 220 (2016), 495–517.
With George Peschke; preprint arXiv:1505.05406.

Algebraically coherent categories, Theory Appl. Categ. 30 (2015), no. 54, 1864–1905.
With Alan Cigoli and James Gray.

Further remarks on the “Smith is Huq” condition, Appl. Categ. Structures 23 (2015), 527–541.
With Nelson Martins-Ferreira; preprint arXiv:1401.5604.

Peri-abelian categories and the universal central extension condition, J. Pure Appl. Algebra 219 (2015), 2506–2520.
With James Gray; preprint arXiv:1404.3067.

On the normality of Higgins commutators, J. Pure Appl. Algebra 219 (2015), 897–912.
With Alan Cigoli and James Gray; preprint arXiv:1312.5474.

On the reflectiveness of special homogeneous surjections of monoids, Categorical Methods in Algebra and Topology, Textos de Matemática (Série B), vol. 46, Departamento de Matemática da Universidade de Coimbra, 2014, pp. 237–244.
With Andrea Montoli and Diana Rodelo; preprint pdf.

Approximate Hagemann-Mitschke co-operations, Appl. Categ. Structures 22 (2014), 1009–1020.
With Diana Rodelo; preprint arXiv:1305.1115.

A decomposition formula for the weighted commutator, Appl. Categ. Structures 22 (2014), 899–906.
With Nelson Martins-Ferreira; preprint arXiv:1304.1331.

Categories vs. groupoids via generalised Mal'tsev properties, Cah. Topol. Géom. Differ. Catég. LV (2014), no. 2, 83–112.
With Nelson Martins-Ferreira; preprint arXiv:1206.2745.

An observation on n-permutability, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 2, 223–230.
With Nelson Martins-Ferreira and Diana Rodelo; preprint arXiv:1306.6523.

A Galois theory for monoids, Theory Appl. Categ. 29 (2014), no. 7, 198–214.
With Andrea Montoli and Diana Rodelo.

Hagemann's theorem for regular categories, J. Homotopy Relat. Struct. 9 (2014) 55–66.
With Diana Rodelo and Zurab Janelidze; preprint Pré-Publicações DMUC 13-14 (2013), 1–15.

Universal central extensions in semi-abelian categories, Appl. Categ. Structures 22 (2014), 253–268.
With José Manuel Casas; preprint arXiv:1302.5501.

The fundamental group functor as a Kan extension, Cah. Topol. Géom. Differ. Catég. LIV (2013), 185–210.
With Tomas Everaert and Julia Goedecke; preprint arXiv:1307.0068.

A characterisation of the “Smith is Huq” condition in the pointed Mal'tsev setting, Cah. Topol. Géom. Differ. Catég. LIV (2013), 163–183.
With Dominique Bourn and Nelson Martins-Ferreira; preprint pdf.

Relative Mal'tsev categories, Theory Appl. Categ. 28 (2013), no. 29, 1002–1021.
With Tomas Everaert, Julia Goedecke and Tamar Janelidze-Gray.

The ternary commutator obstruction for internal crossed modules, Adv. Math. 232 (2013), 571–607.
With Manfred Hartl; preprint arXiv:1107.0954.

Higher central extensions via commutators, Theory Appl. Categ. 27 (2012), no. 9, 189–209.
With Diana Rodelo.

Resolutions, higher extensions and the relative Mal'tsev axiom, J. Algebra 371 (2012) 132–155.
With Tomas Everaert and Julia Goedecke; preprint arXiv:1206.2946.

Relative commutator theory in semi-abelian categories, J. Pure Appl. Algebra 216 (2012) 1791–1806.
With Tomas Everaert; preprint arXiv:1108.3909.

A note on the “Smith is Huq” condition, Appl. Categ. Structures 20 (2012), no. 2, 175–187.
With Nelson Martins-Ferreira; preprint arXiv:1006.1768.

Galois theory and commutators, Algebra Universalis 65 (2011), no. 2, 161–177.
With Tomas Everaert; preprint arXiv:1104.0518.

Homology and central extensions of Leibniz and Lie n-algebras, Homology, Homotopy and Appl. 13 (2011), no. 1, 59–74.
With José Manuel Casas, Emzar Khmaladze and Manuel Ladra.

A note on double central extensions in exact Mal'tsev categories, Cah. Topol. Géom. Differ. Catég. LI (2010), 143–153.
With Tomas Everaert; preprint Pré-Publicações DMUC 09–06 (2009), 1–8.

The third cohomology group classifies double central extensions, Theory Appl. Categ. 23 (2010), no. 8, 150–169.
With Diana Rodelo.

On satellites in semi-abelian categories: Homology without projectives, Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 3, 629–657.
With Julia Goedecke; final pdf (copyright Cambridge Philosophical Society); additional comments.

Simplicial homotopy in semi-abelian categories, J. K-Theory 4 (2009), no. 2, 379–390.
Preprint arXiv:math/0607076; additional comments.

Higher Hopf formulae for homology via Galois Theory, Adv. Math. 217 (2008), 2231–2267.
With Tomas Everaert and Marino Gran.

On the second cohomology group in semi-abelian categories, J. Pure Appl. Algebra 212 (2008), 636–651.
With Marino Gran.

A comparison theorem for simplicial resolutions, J. Homotopy Relat. Struct. 2 (2007), no. 1, 109–126.
With Julia Goedecke.

Model structures for homotopy of internal categories, Theory Appl. Categ. 15 (2005), no. 3, 66–94.
With Tomas Everaert and Rudger Kieboom.

Baer invariants in semi-abelian categories II: Homology, Theory Appl. Categ. 12 (2004), no. 4, 195–224.
With Tomas Everaert; additional comments.

Baer invariants in semi-abelian categories I: General theory, Theory Appl. Categ. 12 (2004), no. 1, 1–33.
With Tomas Everaert; additional comments.

Weak (co)fibrations in categories of (co)fibrant objects, Homology, Homotopy and Appl. 5 (2003), no. 1, 345–386.
With Rudger Kieboom, Gert Sonck and Peter Witbooi.

With Jone Intxaurraga Larrañaga, a translation of an old article written by George Janelidze

G. Z. Janelidze, On satellites in arbitrary categories, Bull. Georgian Acad. Sci. 82 (1976), no. 3, 529–532, in Russian. English translation, September 2008, arXiv:0809.1504.

My Ph.D. thesis, supervised by Rudger Kieboom, defended in January 2006

Homology and homotopy in semi-abelian categories, Ph.D. Thesis, Vrije Universiteit Brussel, 2006, arXiv:math/0607100.

Some lectures

Lectures on non-associative algebras at the Summer School in Algebra and Topology, Louvain-la-Neuve, 12–15 September 2018.

Categorical-algebraic methods in group cohomology at CT2017, Vancouver, 20th July 2017.

Qu'est-ce l'admissibilité de Nelson Martins-Ferreira ? at the Séminaire Itinérant de Catégories of the 31st of October 2015 in Louvain-la-Neuve.

Une approche intrinsèque des produits tensoriels at the Séminaire Itinérant de Catégories dedicated to Jacques Riguet, the 16th of November 2013 in Paris. (Joint work with Manfred Hartl)

Organisation of conferences, workshops, etc.

International Category Theory Conference CT2024, Santiago de Compostela, 23–29 June 2024.
108th Peripatetic Seminar on Sheaves and Logic, with a satellite event on Logic & Algebra, Palermo, 15–17 September 2023.
International Category Theory Conference CT2023, Louvain-la-Neuve, 2–8 July 2023.
Workshop on Categories and Topology, Louvain-la-Neuve, 9 September 2022, on the occasion of Ieke Moerdijk's being appointed the 2022 Chaire de La Vallée Poussin.
Summer School in Algebra and Topology, Louvain-la-Neuve, 11–14 September 2019.
105th Peripatetic Seminar on Sheaves and Logic, with a satellite event on Categorical Methods in Algebra, Palermo, 17–19 May 2019.
Séminaire Itinérant de Catégories, Louvain-la-Neuve, 22 mars 2019.
Summer School in Algebra and Topology, Louvain-la-Neuve, 12–15 September 2018.
102nd Peripatetic Seminar on Sheaves and Logic, Santiago de Compostela, 14–15 January 2018.
5th Workshop on Categorical Methods in Non-Abelian Algebra, Louvain-la-Neuve, 1–3 June 2017, on the occasion of George Janelidze's being appointed the 2017 Chaire de La Vallée Poussin.
Séminaire Itinérant de Catégories, Bruxelles, 27 janvier 2017.
Séminaire Itinérant de Catégories, Louvain-la-Neuve, 31 octobre 2015.
Workshop in Category Theory and Algebraic Topology, Louvain-la-Neuve, September 2015.
97th Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve, 31 January–1 February 2015.
Summer School Category Theory and Algebraic Topology, Lausanne, September 2014.
Séminaire Itinérant de Catégories, Louvain-la-Neuve, 17 mai 2014.
Summer School Category Theory and Algebraic Topology, Louvain-la-Neuve, September 2013.
Séminaire Itinérant de Catégories, Louvain-la-Neuve, 24 mai 2013.
Séminaire Itinérant de Catégories, Louvain-la-Neuve, 19 mai 2012.
Category Theory, Algebra and Geometry, Louvain-la-Neuve, 26–27 May 2011, on the occasion of Ross Street's being appointed the 2011 Chaire de la Vallée Poussin.
89th Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve, 12–13 December 2009.
Categories in Algebra, Geometry and Logic, Brussel, 10–11 October 2008, on the occasion of the sixtieth birthdays of Francis Borceux and Dominique Bourn.