MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.

MSC Codes:
18A40, 18B40
adjoint functor, monoid

Related publications

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

Adjunction of monoids