Aspects of algebraic exponentiation

Abstract

We analyse some aspects of the notion of \emph{algebraic exponentiation} introduced by the second author [16] and satisfied by the category $Gp$ of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category $Gp$, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category.