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中文摘要：
本文首先给出了对合Quantale余核映射的概念，证明了任意子对合Quantale都是某对合Quantale余核映射的象。其次构造出了对合Quantale范畴IQuant中由集合生成的自由对合Quantale的具体结构，证明了遗忘函子U：IQuant→Set有左伴随，并给出了其左伴随函子。最后，证明了IQuant中的单态射恰为单同态，得出了对合Quantale上的余核映射与其在范畴IQuant中的子对象是一一对应的，从而证明了IQuant是良幂的。
英文摘要：
First, the concept of involutive quantic conucleus is given, and it is proved that every sub-involutive quantale is the image of some involutive quantic conucleus. Second, the free involutive quantale generated by a set is constructed and hence the forgetful functor U： IQuant→ Set has a given left adjoint. At last, we proved that the monomorphism in IQuant is precisely the injective homomorphism. And a one-to-one correspondence between the set of all the involutive quantic conucleus on a involutive quantale and the set of all the sub-objects of it in IQuant can be obtained. So, the well-powered fact of IQuant is proved.
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