English

Inverse Sets and Inverse Correspondences Over Inverse Semigroups

Operator Algebras 2024-04-10 v1 Category Theory Group Theory Rings and Algebras

Abstract

In this paper, we introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert CC^*-modules and \Ccorrs in the CC^*-algebra theory. We show that inverse semigroups and inverse correspondences form a bicategory. In this bicategory, two inverse semigroups are equivalent if and only if they are Morita equivalent.

Keywords

Cite

@article{arxiv.2404.06163,
  title  = {Inverse Sets and Inverse Correspondences Over Inverse Semigroups},
  author = {Tomoki Uchimura},
  journal= {arXiv preprint arXiv:2404.06163},
  year   = {2024}
}

Comments

38 pages

R2 v1 2026-06-28T15:48:33.578Z