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Epicompletion in frames with skeletal maps, I: Compact regular frames
 Appl. Categ. Structures
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Epicompletion in frames with skeletal maps, II: Coherent normal archimedean frames
 J. Martínez & Eric R. Zenk
"... Abstract. In previous work it was shown that there is an epireflection ψ of the category of all compact normal, joinfit frames, with skeletal maps, in the full subcategory of frames which are also strongly projectable, and that ψ restricts to the epicompletion ε, which is the absolute reflection on ..."
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Abstract. In previous work it was shown that there is an epireflection ψ of the category of all compact normal, joinfit frames, with skeletal maps, in the full subcategory of frames which are also strongly projectable, and that ψ restricts to the epicompletion ε, which is the absolute reflection on compact regular frames. In the first part of this paper it is shown that ψ is a monoreflection and that the reflection map is, in fact, closed. Restricted to coherent frames and maps, ψA can then be characterized as the least strongly projectable, coherent, normal, joinfit frame in which A can be embedded as a closed, coherent, and skeletal subframe. The second part discusses the role of the nucleus d in this context. On algebraic frames with coherent skeletal maps d becomes an epireflection. Further, it is shown that e = d · ψ epireflects the category of coherent, normal, joinfit frames, with coherent skeletal maps, in the subcategory of those frames which are also regular and strongly projectable, which are epicomplete. The action of e is not monoreflective.
Epicompletion in Frames with Skeletal Maps, IV: Strongly Joinfit Frames
"... Abstract. Earlier work has shown that there is a monoreflection ψ of the category of compact normal, joinfit frames with skeletal frame maps in the subcategory consisting of strongly projectable frames. This article extends the domain of ψ to the strongly joinfit frames. The saturation nucleus s is ..."
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Abstract. Earlier work has shown that there is a monoreflection ψ of the category of compact normal, joinfit frames with skeletal frame maps in the subcategory consisting of strongly projectable frames. This article extends the domain of ψ to the strongly joinfit frames. The saturation nucleus s is a reflection with respect to weakly closed frame maps, in the subcategory of subfit frames. Moreover, s · ψ = ψ · s, on compact normal, joinfit frames with skeletal, weakly closed frame maps, and s · ψ is an epireflection, but not a monoreflection, in the subcategory of strongly projectable, regular frames, all of which are epicomplete. This article builds on work in [MZ08a, MZ08b, M08b]. It is part of an ongoing investigation into epicompletion in various categories of compact frames with skeletal frame homomorphisms. In [MZ08a] it was shown that the absolute of a compact regular frame represents the functorial epicompletion. The epicomplete objects here are the strongly projectable compact regular frames. The objective, in the long run, being to abstract the work of Conrad in [C71] on essential closures of archimedean ℓgroups, and Carrera’s contribution in [Cr04] on the
Czechoslovak Mathematical Journal, 56 (131) (2006), 437–474 DIMENSION IN ALGEBRAIC FRAMES
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