English

Residually finite categories

Category Theory 2019-03-28 v1

Abstract

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite. Moreover, finitely generated residually finite categories are Hopfian and finitely presented residually finite categories have solvable word problem.

Keywords

Cite

@article{arxiv.1903.11488,
  title  = {Residually finite categories},
  author = {Clara Loeh},
  journal= {arXiv preprint arXiv:1903.11488},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-23T08:21:02.094Z