Applied Categorical Structures

, Volume 21, Issue 2, pp 167–180 | Cite as

Essential Completeness in Categories of Completely Regular Frames

Article

Abstract

The basic result here is that certain easily described coreflective subcategories S of the category CRFrm of completely regular frames have unique essential completions determined for each L ∈ S by the S-coreflection of the Booleanization of L. Next, this is shown to apply to several familiar subcategories of CRFrm, and concrete descriptions of the essential completions as well as internal characterizations of essential completeness are then given for these cases. Finally, back to the subcategories S in general, the essential completions in any of these are proved to become the epicomplete reflections in the category derived from S by considering only skeletal maps.

Keywords

Completely regular frame Essential monomorphism Essential completion Strongly monocoreflective subcategory Booleanization of a frame 

Mathematics Subject Classifications (2010)

06F25 54C30 54H10 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Department of Mathematics & Computer ScienceWesleyan UniversityMiddletownUSA

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