Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43640
Title: On exponentiability of étale algebraic homomorphisms
Authors: Clementino, Maria Manuel 
Hofmann, Dirk 
Janelidze, George 
Issue Date: 2013
Publisher: Elsevier
Project: Centro de Matemática da Universidade de Coimbra/FCT 
Serial title, monograph or event: Journal of Pure and Applied Algebra
Volume: 217
Issue: 7
Abstract: In this paper we show that the theorem, by Cagliari and Mantovani, stating that in the category of compact Hausdorff spaces every étale map is exponentiable, can be formulated in a general category Alg(T) of Eilenberg-Moore T-algebras, for a monad T, and proved in case T satisfies the so-called Beck-Chevalley condition. For that, Alg(T) is embedded in the (topological) category RelAlg(T) of relational T-algebras, where a suitable notion of étale morphism can be studied, it is shown that morphisms between T-algebras are exponentiable in RelAlg(T), and, moreover, these exponentials belong to Alg(T) whenever the morphisms are étale.
URI: http://hdl.handle.net/10316/43640
DOI: 10.1016/j.jpaa.2012.10.013
10.1016/j.jpaa.2012.10.013
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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