模糊模范畴中的余极限

运用模糊集的方法和原理, 给出模糊模范畴中余极限的有点式和无点式刻画. 首先, 通过引入模糊模范畴中余积的结构性定理, 得到模糊模范畴中余极限的存在性、 唯一性和结构性定理; 其次, 构造J型图范畴到模糊模范畴上的常量系统函子, 并证明余极限函子与常量系统函子的伴随性; 最后, 根据Hom函子及张量积函子的伴随同构关系, 讨论模糊模范畴中极限与余极限的关系.

Colimit in Category of Fuzzy Modules

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.