Abstract: Using the method and principle of fuzzy sets, we gave the concept of category Set(fL) of L-flou sets, and proved that the category Set(L )  of L-fuzzy sets was isomorphic to the category Set(fL ). According to the isomorphism relationship between the category Set (L ) and the lifting category Set_L(S H) of sheaf structures on the sets category, we obtained the category Set(fL ) was isomorphic to the category Set_L(S H).

Key words: L-fuzzy set, L-flou set, category, sheaf, isomophism