A note on injective hulls of posemigroups

Abstract

In this note, we prove the existence of E≤-injective hulls in the category PoSgr≤ of posemigroups and their submultiplicative order-preserving maps; here E≤ denotes the class of those morphisms h: A → B for which h(a1) … h(an) ≤ h(a) always implies a1 … an ≤ a. The result of this note subsumes the results given by Lambek et al. (2012) and by Zhang and Laan (2014).