The classes of stably-vertical, normal, separable, inseparable, purely inseparable and covering morphisms, defined in categorical Galois theory, are characterized for the reflection of the variety of commutative semigroups into its subvariety of semilattices. It is also shown that there is an inseparable-separable factorization, but there is no monotone-light factorization.
Keywords: Commutative semigroups, semilattices, admissible reflection, covering morphisms, stably-vertical morphisms, normal morphisms, inseparable-separable factorization
2010 MSC: 18C99, 08B99, 20M07
Theory and Applications of Categories, Vol. 28, 2013, No. 33, pp 1153-1169.