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arXiv · 2608.23866

The Cofree Functor on G-Sets and Its Approximations

Frank Murphy-Hernandez
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Abstract

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.

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Frank Murphy-Hernandez. 2026-08-24. The Cofree Functor on G-Sets and Its Approximations. https://arxiv.org/abs/2608.23866

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