The Grouplike Functor and Monoidal Adjunctions

@misc{murphyhernandez2026grouplike,
  title = {{The Grouplike Functor and Monoidal Adjunctions}},
  author = {Frank Murphy-Hernandez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14163},
  eprint = {2609.14163},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14163},
}

TY  - UNPB
TI  - The Grouplike Functor and Monoidal Adjunctions
AU  - Frank Murphy-Hernandez
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14163
UR  - https://arxiv.org/abs/2609.14163
AB  - We construct a categorification of the functor of grouplike elements of a Hopf algebra in the setting of braided monoidal categories. Given a braided bistrong monoidal functor admitting a right adjoint, we define a functor assigning to each Hopf monoid a group object obtained as a subobject of its underlying object by means of finite limits. We prove that this construction is functorial and provides a right adjoint to the induced free Hopf monoid functor, thereby extending the classical correspondence between groups and grouplike elements of Hopf algebras to a categorical setting.
ER  -