Some Classes of Quantale Morphisms

Abstract & Overview

This paper concerns some types of coherent quantale morphisms: Baer, minimalisant, quasi rigid, quasi r- and quasi morphisms. Firstly, we study how the reticulation functor preserves the properties that define these types of quantale morphisms. Secondly, we prove some characterization theorems for quasi rigid, quasi r- and quasi morphisms. These theorems extend some results existing in the literature of ring extensions and frame extensions.