ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF VARIETY-BASED TOPOLOGICAL SYSTEMS

Abstract

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

<span style="font-size: xx-small; font-family: CMBX8;">TopSys</span>

of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalued) topology can be embedded into algebra.