Fuzzy sets and sheaves. Part I - Basic concepts
This essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory, respectively, of the theory of complete Omega-valued sets. Hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect. Part I of this essay divided into a series of two papers presents such basic concepts as Omega-valued equalities, espaces etales, singleton monad, the change of base and the subobject classifier axiom. The application of these tools to the sheaf-theoretic foundations of fuzzy sets will appear in Part II. (C) 2006 Elsevier B.V. All rights reserved.
complete omega-valued sets omega-valued sets espace etale singleton monad category theory membership functions geometric morphisms