Epicompletion in Frames with Skeletal Maps,III: When Maps are Closed |
| |
Authors: | Jorge Martínez |
| |
Institution: | (1) Department of Mathematics, Wesleyan University, Middletown, CT 06459, USA;(2) Department of Mathematics, University of Florida, Box 118105, Gainesville, FL 32611-8105, USA |
| |
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, 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|