Topological systems versus attachment relations

Abstract

The manuscript makes a category-theoretic comparison between the concepts of topological system of S. Vickers and attachment relation of C. Guido. With the help of the recent definition of the notions in the framework of an arbitrary variety of algebras, we consider functorial relationships between the categories of such generalized structures, and the link of the obtained functors to both spatialization and localification procedure introduced by S. Vickers for topological systems.

Keywords:

• Adjoint functor
• algebra
• attachment relation
• embedding functorp
• localification of topological systems
• spatialization of topological systems
• topological system
• topological theory
• variety of algebras

Mathematics Subject Classification (2010):

• 03E72
• 54A40
• 18B99
• 18B30