Universal central extensions in semi-abelian categories

TL;DR

This paper explores the concept of universal central extensions within semi-abelian categories, introducing a new condition on the composition of central extensions and analyzing its applicability across different categories.

Contribution

It introduces a new fundamental condition on the composition of central extensions and examines its validity in various semi-abelian categories.

Findings

Identifies categories satisfying the new composition condition

Provides examples of categories that do and do not satisfy the condition

Advances understanding of universal central extensions in semi-abelian contexts

Abstract

Basing ourselves on Janelidze and Kelly's general notion of central extension, we study universal central extensions in the context of semi-abelian categories. We consider a new fundamental condition on composition of central extensions and give examples of categories which do, or do not, satisfy this condition.