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A note on injective hulls of posemigroups

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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.

http://www.tac.mta.ca/tac/volumes/32/7/32-07.pdf

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