Localification procedure for affine systems. (English) Zbl 1326.18003
The paper generalizes the concept of an affine set and an affine system. It is proved that the category of affine sets is isomorphic to a full coreflective subcategory of affine systems. A necessary and sufficient condition is given for the dual category of the variety of algebras whose objects underly the structure of affine sets to be isomorphic to a full reflective subcategory of affine systems. As a consequence, the sobriety-spatial equivalence for affine sets is obtained. A sufficient condition for the category of separated affine sets to make a reflective subcategory of the category of affine sets is shown. Illustrating examples are presented.
Reviewer: Václav Koubek (Praha)
MSC:
18B99 | Special categories |
18B30 | Categories of topological spaces and continuous mappings (MSC2010) |
18C10 | Theories (e.g., algebraic theories), structure, and semantics |
08B99 | Varieties |