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.     

Localization of Universal Problems. Local Colimits

The notion of the root of the category, which is a minimal (in a precise sense) weakly coreflective subcategory, is introduced in view of defining local solutions of universal problems: If U is a functor from C to C and c an object of C, the root of the comma-category c|U is called a U-universal root generated by c; when it exists, it is unique (up to isomorphism) and determines a particular form of the locally free diagrams defined by Guitart and Lair. In this case, the analogue of an adjoint functor is an adjoint-root functor of U, taking its values in the category of pro-objects of C. Local colimits are obtained if U is the insertion from a category into its category of ind-objects; they generalize Diers' multicolimits. Applications to posets and Galois theory are given.