Injective hulls for ordered algebras

We study the injectivity of ordered algebras with respect to the class of homomorphisms that are order-embeddings and one more class of morphisms. We do this in the category where morphisms need not be homomorphisms, but satisfy a condition which is weaker than operation-preservation. In this setting, the injective objects turn out to be precisely sup-algebras. We also show how to construct injective hulls of ordered algebras satisfying certain conditions.