Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 631-645, 2007

# Extensional subobjects in categories of $\Omega$-fuzzy sets

## Jiri Mockor

Jiri Mockor, University of Ostrava, Department of Mathematics and Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic, e-mail: Jiri.Mockor@osu.cz

Abstract: Two categories $\Set$ and $\Setf$ of fuzzy sets over an $MV$-algebra $\Omega$ are investigated. Full subcategories of these categories are introduced consisting of objects $(\sub(A,\delta)$, $\sigma)$, where $\sub(A,\delta)$ is a subset of all extensional subobjects of an object $(A,\delta)$. It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

Keywords: $MV$-algebras, similarity relation, quasi-reflective subcategory

Classification (MSC 2000): 06D35, 18A40

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