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.

Keywords

• ordered σ-algebra
• lax morphism
• sup-lattice
• injective hull
• 06fxx
• 08b30
• 08c05