We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks, string theory, loop quantum gravity, and topological quantum field theory. Our chronology ends around 2000, with just a taste of later developments such as open...

Some known compactness notions and separation axioms already given in Chang-fuzzy topological spaces are extended to a more general context of categories where I -topological spaces on arbitrary I -sets are de3ned. The invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated. c © 2002 Elsevier ...

In the paper we introduce the notion of S-nets, S a non-empty construct , as a generalization of the usual nets. S-net spaces and continuous maps between them are then deened in a natural way. For S-net spaces we introduce a number of axioms and study the categories obtained. We nd some topological and cartesian closed categories of S-net spaces and describe their relations to certain known top...

In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topo-logical functor is similar to (but not the same) the existing notions in the literature (see [2] 7.3), and it aims at the same examples. In our sense, a (pre) topological functor is a functor that creates cartesian families. A topological functor is, ...