Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

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...

Following the point-set lattice-theoretic (poslat) approach to topology of S. E. Rodabaugh [11], we introduced a more general way to do categorical (fuzzy) topology under the name of categorically-algebraic (catalg) topology [12], which unified many lattice-valued topological settings, and provided the means of intercommunication between different such frameworks. Moreover, motivated by the res...

A notion of central importance in categorical topology is that of topological functor. A faithful functor E → B is called topological if it admits cartesian liftings of all (possibly large) families of arrows; the basic example is the forgetful functor Top→ Set. A topological functor E → 1 is the same thing as a (large) complete preorder, and the general topological functor E → B is intuitively...