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arXiv · 2109.06278

Semi-biproducts of monoids

Nelson Martins-Ferreira
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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.

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Nelson Martins-Ferreira. 2021-09-13. Semi-biproducts of monoids. https://arxiv.org/abs/2109.06278

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