Open Mathematics (Dec 2019)
Injective hulls of many-sorted ordered algebras
Abstract
This paper is devoted to the study of injectivity for ordered universal algebras. We first characterize injectives in the category OALΣ⩽$\begin{array}{} \displaystyle {\mathsf{OAL}_{{\it\Sigma}}^{\leqslant}} \end{array}$ of ordered Σ-algebras with lax morphisms as sup-Σ-algebras. Second, we show that every ordered Σ-algebra has an σ⩽-injective hull, and give its concrete form.
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