Abstract: Using the method and principle of fuzzy sets, the author gave by virtue pointwise and pointless depiction of colimit in the category of fuzzy modules. Firstly, by introducing the structural theorem of the coproduct in the category of fuzzy modules, the author obtained existence, uniqueness and structural theorem
 of colimit in the category of fuzzy modules. Secondly, the author constructed a constant system functor from the category of shapes of J to the category of fuzzy modules, and proved adjoint pair of a colimit functor and constant system functor. Finally, according to the adjoint isomorphisms relationship between the functor Hom and the tensor product functor , the author discussed the relationship between limits and colimits in the category of fuzzy modules.

Key words: adjoint, colimit, category, limit, fuzzy module