Morphisms and Pushouts in Compact Normal Joinfit Frames

摘要

KNJ is the category of compact normal joinfit frames and frame homomorphisms and KReg is the coreflective subcategory of compact regular frames. This work investigates KNJ through its interaction with KReg via the coreflection rho. A KNJ morphism phi: F -> M is P-essential if phi is skeletal and the map between the frames of polars, P(phi): PF -> PM defined by P(phi)(p)=phi(p)(perpendicular to perpendicular to), is a boolean isomorphism. The P-essential morphisms in KNJ are closely related to the essential embeddings in KReg. We provide a characterization of the P-essential morphisms in KNJ and a connection to the essential embeddings in KReg. Further results about the preservation of joinfitness, the factorization of morphisms, and monomorphisms in KNJ are provided. Moreover, in the category of KNJ objects and skeletal frame homomorphisms, KNJS, we construct for F is an element of KNJ and phi: rho F -> H (an arbitrary KReg essential embedding of ?F) the KNJS pushout of phi: rho F -> F and phi: rho F -> H. Lastly, we investigate the epimorphisms and epicomplete objects in KNJS.