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Title: On the representability of actions for topological algebras
Authors: Borceux, Francis 
Clementino, Maria Manuel 
Montoli, Andrea 
Issue Date: 2014
Publisher: DMUC - Textos de Matemática
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Serial title, monograph or event: Categorical Methods in Algebra and Topology: Special Volume in Honour of Manuela Sobral
Volume: 46
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 quasi-locally 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).
Rights: openAccess
Appears in Collections:I&D CMUC - Livros e Capítulos de Livros

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