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Applied Categorical Structures

, Volume 24, Issue 5, pp 733–742 | Cite as

On Exponentiable Morphisms in Classical Algebra

  • Maria Manuel Clementino
  • Dirk Hofmann
  • George Janelidze
Article
  • 67 Downloads

Abstract

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphisms in ideal determined varieties and extend this to ideal determined categories. Finally, we give a complete characterization of exponentiable homomorphisms of semimodules over semirings.

Keywords

Exponentiable morphism Taut monad Subtractive variety Ideal determined variety Semimodule 

Mathematics Subject Classifications (2010)

18C15 18C20 08A62 16Y60 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Maria Manuel Clementino
    • 1
  • Dirk Hofmann
    • 2
  • George Janelidze
    • 3
  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.CIDMA, Department of MathematicsUniversity of AveiroAveiroPortugal
  3. 3.Department of Mathematics and Applied MathematicsUniversity of Cape TownCape TownSouth Africa

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