This paper introduces a generalization of the concept of Set category
introduced in [10] by constructing the category - whose objects are
small ℒ - fuzzy sets in which the characteristic functions takes its values from
a complete distributive latt
ice, and its arrows are ℒ - fuzzy maps. After that
we construct a functor - between these two categories, in a
way that forgets the fuzziness of sets and maps, and formalizing the inclusion
functor - .
In addition, we study of the applications of universal arrows in category
- , and getting back to the classical state and comparing it with that
introduced in [10].
