Corentin Vienne (Università di Milano) will give a talk on
When is the composition of normal monomorphisms stable?
Abstract:
It is well known that, in general, a normal subgroup of a normal subgroup need not be normal. In other words, in the category of groups, normality is not transitive. By contrast, in the category of abelian groups, or more generally in any abelian category, normality is transitive.
In this talk, we exhibit some non-abelian categories in which the composition of normal monomorphisms is stable, and we explore the categorical characterisations and consequences of this property in the semi-abelian context.
This is joint work with X. García-Martínez, J.R.A. Gray, M.A. Hoefnagel and T. Van der Linden.
References
[1] X. García-Martínez, J. R. A. Gray, M. A. Hoefnagel, T. Van der Linden, and C. Vienne. Categorical algebraic aspects of Heyting semilattices, in preparation (2025).
[2] C. Vienne. Categorical-algebraic conditions in semi-abelian categories, PhD Thesis, UCLouvain (2025).