Fuzzy sets, sheaves, and topoi

There have been a number of attempts to provide a categorical foundation for fuzzy sets. One inescapable limitation seems to be that fuzzy sets cannot form a topos without restrictions placed on the underlying lattice or on the associated “equality”. This paper reviews work in this area and concludes that categorical unification of fuzzy sets, at least of the kinds described to date, may be unnecessary and even inappropriate given the varieties of “real-world” semantics that fuzzy set theory needs to support