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 -modules and \Ccorrs in the -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.
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