What is a semi-abelian category?
Event details
| Date | 15.03.2013 |
| Hour | 14:15 › 15:30 |
| Speaker | Marino Gran (Université Catholique de Louvain-la-Neuve) |
| Location |
MA 10
|
| Category | Conferences - Seminars |
The problem of finding an axiomatic context capturing some typical
properties of the category of groups was already mentioned by S. Mac Lane
in the article [1]. Only recently the introduction of the notion of
semi-abelian category [2] made it possible to treat many fundamental
properties the categories of groups, Lie algebras, crossed modules and
compact groups have in common, in a similar way to the one the notion of
abelian category allows for a unified treatment of module categories and
of their categories of sheaves. The theory of semi-abelian categories
provides a suitable categorical setting to treat some fundamental aspects
of non-abelian homological algebra, radical theory and commutator theory.
This introductory talk will focus on some basic aspects of the theory, and
on a couple of more recent results obtained in collaboration with T.
Everaert, T. Van der Linden and M. Duckerts [3,4].
References
[1] S. Mac Lane, Duality of groups, Bull. Am. Math. Soc. 56 (6), 486-516
(1950)
[2] G. Janelidze, L. Marki and W. Tholen, Semi-abelian categories, J. Pure
Appl. Algebra 168, 367-386 (2002)
[3] T. Everaert, M. Gran and T. Van der Linden, Higher Hopf formulae for
homology via Galois Theory, Adv. Math. 217, 2231-2267 (2008)
[4] M. Duckerts, T. Everaert and M. Gran, A description of the fundamental
group in terms of commutators and closure operators, J. Pure Appl. Algebra
216, 1837-1851 (2012)
properties of the category of groups was already mentioned by S. Mac Lane
in the article [1]. Only recently the introduction of the notion of
semi-abelian category [2] made it possible to treat many fundamental
properties the categories of groups, Lie algebras, crossed modules and
compact groups have in common, in a similar way to the one the notion of
abelian category allows for a unified treatment of module categories and
of their categories of sheaves. The theory of semi-abelian categories
provides a suitable categorical setting to treat some fundamental aspects
of non-abelian homological algebra, radical theory and commutator theory.
This introductory talk will focus on some basic aspects of the theory, and
on a couple of more recent results obtained in collaboration with T.
Everaert, T. Van der Linden and M. Duckerts [3,4].
References
[1] S. Mac Lane, Duality of groups, Bull. Am. Math. Soc. 56 (6), 486-516
(1950)
[2] G. Janelidze, L. Marki and W. Tholen, Semi-abelian categories, J. Pure
Appl. Algebra 168, 367-386 (2002)
[3] T. Everaert, M. Gran and T. Van der Linden, Higher Hopf formulae for
homology via Galois Theory, Adv. Math. 217, 2231-2267 (2008)
[4] M. Duckerts, T. Everaert and M. Gran, A description of the fundamental
group in terms of commutators and closure operators, J. Pure Appl. Algebra
216, 1837-1851 (2012)
Links
Practical information
- Informed public
- Free
Organizer
- Kathryn Hess