范畴中morphic对象的推广

Promotion of Quasi-mophic Objects in Some Categories

为了推广范畴中的morphic对象,通过引入范畴中的拟-morphic对象,给出了拟-morphic对象的一些等价刻画,并讨论了拟-morphic元与正则元的关系,推广其在p-exact范畴Abelian范畴中的若干性质:设A为p-exact范畴中的拟-morphic对象,则A的所有子对象均同构于A的一个像当且仅当A的所有像均同构于A的所有子对象;设C和D均为Abelian范畴,F∶C→D为完全忠实正合函子,且A∈Ob C,则A为拟-morphic的当且仅当F(A)也为拟-morphic的。进一步说明了范畴中的拟-morphic对象为morphic对象的真正推广。

By introducing the quasi-morphic objects in the category, some equivalent characterizations of the quasi-morphic objects are given, and the relationship between the quasi-morphic element and the regular elem ent is discussed, some properties of quasi-morphic objects in the p-exact and Abelian category are promoted. It is proved that let A be a quasi-morphic object in the p-exact category, then all images of A are isomorphic to an image of A if and only if all images of A are isomorphic to all sub-objects of A;let C and D be Abelian categories, F : C → D is a completely faithful exact functor, and A∈Ob C, then A is quasi-morphic if and only if F(A) is also quasi-morphic. It further explains that the quasi-morphic objects in the category are the real promotion of morphic objects.