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Pointed semibiproducts of monoids

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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.

http://www.tac.mta.ca/tac/volumes/39/6/39-06.pdf

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