Please use this identifier to cite or link to this item:
https://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: | https://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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JPAA_CHJ_etale_algebraic_homomorphisms_revised.pdf | 174.96 kB | Adobe PDF | View/Open |
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