Extensional subobjects in categories of Ω-fuzzy sets

Abstract

Two categories Set(Ω) and SetF(Ω) of fuzzy sets over an MV-algebra Ω are investigated. Full subcategories of these categories are introduced consisting of objects (sub(A, δ), σ), where sub(A, δ) is a subset of all extensional subobjects of an object (A, δ). It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.