We find the injective hulls of partially ordered monoids in the category whose objects are po-monoids and submultiplicative order-preserving functions. These injective hulls are with respect to a special class of monics called ``embeddings''. We show as well that the injective objects with respect to these embeddings are precisely the quantales.
Keywords: partially ordered monoids, injectives
2000 MSC: 06F05, 06F07, 08B30
Theory and Applications of Categories, Vol. 26, 2012, No. 13, pp 338-348.