Pure Galois theory in categories

Homology and central extensions of Leibniz and Lie $n$-algebras

“…Together with the classes of extensions in A and B, this adjunction forms a Galois structure in the sense of Janelidze ([3]; see also [19]). The coverings with respect to this Galois structure are the central extensions introduced in [20] (see Section 2.7 below for an explicit definition).…”

Galois theory and double central extensions

“…gives rise to a natural Galois structure in the sense of the categorical Galois theory of Janelidze [3]. This Galois structure Γ determines a class of homomorphisms, called Γ-coverings, which turn out to be exactly the central extensions of groups, i.e.…”

Comprehensive factorisation systems

“…Janelidze [21] defines Galois theory in terms of a given reflective subcategory (an axiomatisation of the full subcategory of "discrete" objects). He developes an abstract notion of covering extension which subsumes the topological coverings and the central extensions in algebra [22] as special cases, and obtains a Galois-type classification for covering extensions with fixed codomain.…”