2023/07/10 by Janelidze, George, Sobral, Manuela
#06D75 #06E20 #06E75 #16Y60 #18A30 #18A40 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2307.04383
For a commutative semiring S, by an S-algebra we mean a commutative semiring A equipped with a homomorphism from S to A. We show that the subvariety of S-algebras determined by the identities 1+2x=1 and x2=x is closed under non-empty colimits. The (known) closedness of the category of Boolean rings and of the category of distributive lattices under non-empty colimits in the category of commutative semirings both follow from this general statement.