Pointed semibiproducts of monoids

Nelson Martins-Ferreira

A new notion of a (pointed) semibiproduct is introduced, which, in the case of groups amounts to an extension equipped with a set-theoretical section. When the section is a group homomorphism then a pointed semibiproduct is the same as a group split extension. The main result of the paper is a characterization of pointed semibiproducts of monoids using a structure that is a generalization of the action that is used in the definition of a semidirect product of groups.

Keywords: Semibiproduct, biproduct, semidirect product of groups and monoids, pointed semibiproduct, semibiproduct extension, pointed monoid action system, Schreier extension

2020 MSC: 18G50, 20M10, 20M32

Theory and Applications of Categories, Vol. 39, 2023, No. 6, pp 172-185.

Published 2023-02-17.


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