ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF VARIETY-BASED TOPOLOGICAL SYSTEMS

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.