Injective hulls of partially ordered monoids

J. Lambek, Michael Barr, John F. Kennison, R. Raphael

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.

Published 2012-07-06.

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