Central extensions in semi-abelian categories

Abstract

In the context of semi-abelian categories, we develop some new xaspects of the categorical theory of central extensions by Janelidze and Kelly. If C is a semi-abelian category and X is any admissible subcategory we give several characterizations of trivial and central extensions. The notion of central extension becomes intrinsic when X is the subcategory of the abelian objects in C . We apply these results to the category of internal groupoids in a semi-abelian category. As a very special case, we get the known description of central extensions for crossed modules.