2021/09/13 by Martins-Ferreira, Nelson
#18G50 #20M10 #20M32 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.06278
It is shown that the category of semi-biproducts of monoids is equivalent to the category of 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.