English

Actions of pro-groups and pro-rings

Group Theory 2026-05-08 v1 Category Theory Rings and Algebras

Abstract

We give an explicit description of internal actions in the semi-abelian categories of pro-groups and non-unital pro-rings in terms of actions of group objects and ring objects in Pro(Set)\mathrm{Pro}(\mathbf{Set}), as well as in some related categories. Also, we show that a similar result fails for Lie algebras.

Keywords

Cite

@article{arxiv.2205.13336,
  title  = {Actions of pro-groups and pro-rings},
  author = {Egor Voronetsky},
  journal= {arXiv preprint arXiv:2205.13336},
  year   = {2026}
}