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Title: On Exponentiable Morphisms in Classical Algebra
Author: Clementino, Maria Manuel
Hofmann, Dirk
Janelidze, George
Keywords: Exponentiable morphism
Taut monad
Subtractive variety
Ideal determined variety
Issue Date: Oct-2016
Publisher: Springer Verlag
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 ``\'{e}tale 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 exponential homomorphisms of semimodules over semirings.
Peer review: yes
DOI: 10.1007/s10485-016-9458-7
ISSN: 0927-2852
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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