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 (latticevalu...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

A workshop on "New Connections between Mathematics and Computer Science" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England from 20-24 November 1995. The workshop was supported by the Engineering and Physical Science Research Council of the United Kingdom, the London Mathematical Society and Hewlett-Packard's Basic Research Institute in the Mathematical Scien...