A note on idempotent semirings
Category Theory
2023-07-11 v1
Abstract
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 x^2=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.
Cite
@article{arxiv.2307.04383,
title = {A note on idempotent semirings},
author = {George Janelidze and Manuela Sobral},
journal= {arXiv preprint arXiv:2307.04383},
year = {2023}
}
Comments
4 pages