2016/04/14 by Aaron Gray, Gray, Aaron, Keith Pardue +1
Computer Science · Mathematics · #18D35 #Advanced Algebra and Logic #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1604.03999
openalex publication_date 2016/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study monoids equipped with a second binary operation that captures the structure of the endomorphisms of an object X such that X=X× X. We construct a universal monoid of this type and examine some of its rich combinatorial structure. We show that if X has a nontrivial endomorphism and X=X× X, then every finite monoid has a faithful action on X.