Open Access
december 2012 Aspects of algebraic exponentiation
Dominique Bourn, James R. A. Gray
Bull. Belg. Math. Soc. Simon Stevin 19(5): 821-844 (december 2012). DOI: 10.36045/bbms/1354031552


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.


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Dominique Bourn. James R. A. Gray. "Aspects of algebraic exponentiation." Bull. Belg. Math. Soc. Simon Stevin 19 (5) 821 - 844, december 2012.


Published: december 2012
First available in Project Euclid: 27 November 2012

zbMATH: 1264.18003
MathSciNet: MR3009018
Digital Object Identifier: 10.36045/bbms/1354031552

Primary: 13A99 , 17B99 , 18A40 , 18C15 , 18D15 , 20A05

Keywords: Beck-Chevalley condition , ‎centralizer‎ , Fibration of points , locally cartesian closed category , Mal'cev and protomodular categories , unital

Rights: Copyright © 2012 The Belgian Mathematical Society

Vol.19 • No. 5 • december 2012
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