caa a22 4500 445378964 CHVBK 20180317143011.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10485-009-9194-3 doi (NATIONALLICENCE)springer-10.1007/s10485-009-9194-3 Martínez Jorge Department of Mathematics, University of Florida, Box 118105, 32611-8105, Gainesville, FL, USA aut Epicompletion in Frames with Skeletal Maps, III: When Maps are Closed [Elektronische Daten] [Jorge Martínez] 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, ψ A 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. Springer Science+Business Media B.V., 2009 Epicompletion nationallicence Skeletal and closed frame maps nationallicence Strongly projectable frames nationallicence Monoreflection nationallicence Applied Categorical Structures Springer Netherlands 19/2(2011-04-01), 489-504 0927-2852 19:2<489 2011 19 10485 https://doi.org/10.1007/s10485-009-9194-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-009-9194-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Martínez Jorge Department of Mathematics, University of Florida, Box 118105, 32611-8105, Gainesville, FL, USA aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/2(2011-04-01), 489-504 0927-2852 19:2<489 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445378964 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer