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Adjunction of monoids
Dimitry A. Leites and Vladimir Molotkov
Let M and N be monoids considered as categories with the only object. Let f:M-->N and g: N--> M be morphisms of monoids, considered as functors. Let the functor f be left adjoint to g. In 1976, E. Manes, in the book "Algebraic Theories" (Springer), posed the question: Is it true that f (or g) is always an isomorphism? Here we show that the answer is NO.