Aspects of algebraic exponentiation
  We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category of groups, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category. 
Dominique Bourn and James R.A. Gray
math.CT