ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF VARIETY-BASED TOPOLOGICAL SYSTEMS

نویسندگان
Solovyov, Sergey A. ID 1

1 Department of Mathematics, University of Latvia, Zellu iela 8, LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia

doi
10.22111/ijfs.2011.295
چکیده

Motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by S. Vickers, providing an algebraic and a coalgebraic category of the new structures. As a result, the nature of the category   TopSys   of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalued) topology can be embedded into algebra.

کلیدواژه‌ها
Algebra, (Co)algebraic category, (Co)re ective subcategory, Latticevalued topology, Powerset operator, S-quantale, Topological category, Topological system, Variety