Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	On the representability of actions for topological algebras
Publication Date:	2014-06-16
Authors:	- Francis Borceux - Maria Manuel Clementino - Andrea Montoli
Abstract:	The actions of a group B on a group X correspond bijectively to the group homomorphisms B → Aut(X), proving that the functor "actions on X" is representable by the group of automorphisms of X. Making the detour through pseudotopological spaces, we generalize this result to the topological case, for quasilocally compact groups and some other algebraic structures. We investigate next the case of arbitrary topological algebras for a semi-abelian theory and prove that the representability of topological actions reduces to the preservation of coproducts by the functor Act(−,X).
Institution:	DMUC 14-19
Online version:	http://www.mat.uc.pt...prints/eng_2014.html
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