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MiS Preprint
128/2006

Adjunction of monoids

Dimitry A. Leites and Vladimir Molotkov

Abstract

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.

Received:
Nov 12, 2006
Published:
Nov 12, 2006
MSC Codes:
18A40, 18B40
Keywords:
adjoint functor, monoid

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Preprint
2006 Repository Open Access
D. A. Leites and Vladimir Molotkov

Adjunction of monoids