Universal groups on semilattices of reversible cancellative semigroups

LetS be a semigroup which is a semilattice Ω of reversible cancellative semigroupsS α, α∈Ω. This paper studies the relationship between the universal groupG onS and the universal groupsG α onS α. We also show that the universal homorphismsf α∶S α→G α, α∈Ω fromS α to the category of groups combine to a homomorphismf∶S→G ofS into the category of groups.