# A note on injective hulls of posemigroups

## Changchun Xia, Shengwei Han, Bin Zhao

In this note, we prove the existence of $E_\leq$-injective hulls in the category $PoSgr_\leq$ of posemigroups and their submultiplicative order-preserving maps; here $E_\leq$ denotes the class of those morphisms $h : A \to B$ for which $h(a_1)...h(a_n)\leq h(a)$ always implies $a_1...a_n\leq a$. The result of this note subsumes the results given by Lambek et al. (2012) and by Zhang and Laan (2014).

Keywords: partially ordered semigroup, quantale, quantic nucleus, injective hull

2010 MSC: 06F05, 06F07, 08B30

Theory and Applications of Categories, Vol. 32, 2017, No. 7, pp 253-257.

Published 2017-02-08.

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