正向极限的等价刻画及应用

Equivalent Characterizations of Direct Limits and Applications

通过构造新的范畴,分别从广义推出、始对象和可表函子等概念出发,给出一般范畴中正向极限的3个等价刻画.最后利用等价刻画给出模范畴正向极限存在性的一种新证明.

Starts from the known concepts of generalized pushout, origin object and representable functor, gives three equivalent characterizations for direct limits of general categories by constructing new categories. Finally, gives a new proof for the existence of direct limits in module category with the equivalent characterizations.