AI 中文总结
本文研究群作用范畴上的余自由函子，引入与子群相关的函子并发展其理论，探讨对应余反射子范畴，证明由余自由伴随诱导的余单子可对群分类。
AI 中文摘要
我们研究群作用范畴上的余自由函子，考察其范畴论与组合性质。受该构造启发，我们引入与子群相关的一族函子，通过群作用的对应余反射子范畴发展其理论。最后，我们研究由余自由伴随在集合范畴诱导的余单子，并证明其可对群进行分类。
英文摘要
We study the cofree functor on the category of group actions and examine its categorical and combinatorial properties. Motivated by this construction, we introduce a family of functors associated with subgroups and develop their theory through a corresponding coreflective subcategory of group actions. Finally, we investigate the comonad in the category of sets induced by the cofree adjunction and prove that it classifies the groups.
Comments22 pages
