Geodesic
Extensional subobjects in categories of $\Omega$-fuzzy sets
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 631-645 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Two categories $\mathbb{Set}(\Omega )$ and $\mathbb{SetF}(\Omega )$ of fuzzy sets over an $MV$-algebra $\Omega $ are investigated. Full subcategories of these categories are introduced consisting of objects $(\mathop {{\mathrm sub}}(A,\delta )$, $\sigma )$, where $\mathop {{\mathrm sub}}(A,\delta )$ 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.
Two categories $\mathbb{Set}(\Omega )$ and $\mathbb{SetF}(\Omega )$ of fuzzy sets over an $MV$-algebra $\Omega $ are investigated. Full subcategories of these categories are introduced consisting of objects $(\mathop {{\mathrm sub}}(A,\delta )$, $\sigma )$, where $\mathop {{\mathrm sub}}(A,\delta )$ 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.
Classification : 03E72, 06D35, 18A40
Keywords: $MV$-algebras; similarity relation; quasi-reflective subcategory 
@article{CMJ_2007_57_2_a7,
     author = {Mo\v{c}ko\v{r}, Ji\v{r}{\'\i}},
     title = {Extensional subobjects in categories of $\Omega$-fuzzy sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {631--645},
     year = {2007},
     volume = {57},
     number = {2},
     mrnumber = {2337619},
     zbl = {1174.06320},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a7/}
}
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Močkoř, Jiří. Extensional subobjects in categories of $\Omega$-fuzzy sets. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 631-645. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a7/