Sheaf coalgebras and duality

Coalgebras, Stone Duality, Modal Logic

A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand coalgebras as well as Stone duality. So we will need to learn something about modal logic, about S...

Colby]Fuller Duality between Coalgebras

w x In 8 , K. Morita introduced a useful notion of duality between categories of modules, usually called ‘‘Morita duality.’’ He proved that every duality is given by contravariant hom functors defined by a bimodule which is an injective cogenerator for both categories of modules. On the other hand, the equivalences between categories of comodules over a coalgebra w x were characterized by M. Ta...

Duality for Some Categories of Coalgebras

The duality between vertex operator algebras and coalgebras, modules and comodules

We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corresponding comodule structures, as well as when various comodules carry module structure.

Some Properties of Sheaf-solutions of Sheaf Fuzzy Control Problems

In this paper we present some results on the dependence of sheafsolutions of sheaf fuzzy control problems on variation of fuzzy controls.