Semi-biproducts of monoids
Abstract
It is shown that the category of \emph{semi-biproducts} of monoids is equivalent to the category of \emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained through generalizing a biproduct of commutative monoids. By dropping commutativity and requiring some of the homomorphisms in the biproduct diagram to be merely identity-preserving maps, we obtain a semi-biproduct. A pseudo-action is a new notion as well. It consists of three ingredients: a pre-action, a factor system and a correction system. In the category of groups all correction systems are trivial. This is perhaps the reason why this notion, to the author's best knowledge, has never been considered before.
Cite
@article{arxiv.2109.06278,
title = {Semi-biproducts of monoids},
author = {Nelson Martins-Ferreira},
journal= {arXiv preprint arXiv:2109.06278},
year = {2021}
}
Comments
21 pages. arXiv admin note: substantial text overlap with arXiv:2002.05985