P-Essential Reflections and Hull Classes

kNJ (resp., kNJG) is the category of compact, normal joint frames with frame (resp., skeletal frame) homomorphisms. kReg (resp., KRegG) is the category of compact, regular frames with frame (resp., skeletal frame) homomorphisms. We utilize the regular monocoreflection p to investigate the morphisms (objects) of kNJ and kReg, introduce the concept of a kNJ hull class, and investigate the relationship between the kReg and kNJ hull classes. In addition, we introduce the concept of a P -essential reflection on kNJ and exhibit a correspondence between certain reflective subcategories of kRegG and kNJG. Lastly, we apply our results to extend the concept of a polar function (functorial polar function) to the category kNJ.