Higher Central Extensions in Mal'tsev Categories

TL;DR

This paper extends the concept of higher central extensions from semi-abelian to exact Mal'tsev categories, broadening the categorical framework for Galois theory applications.

Contribution

It generalizes the notion of higher central extensions to exact Mal'tsev categories, expanding the theoretical landscape beyond semi-abelian categories.

Findings

Extended higher central extensions to Mal'tsev categories

Unified categorical framework for Galois theory

Broadened applicability of covering morphisms

Abstract

Higher dimensional central extensions of groups were introduced by G. Janelidze as particular instances of the abstract notion of covering morphism from categorical Galois theory. More recently, the notion has been extended to and studied in arbitrary semi-abelian categories. In this article, we further extend the scope to exact Mal'tsev categories and beyond.