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<p>We introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert C*-modules and C*-correspondences in the theory of C*-algebras. 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.</p>

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Inverse Sets and Inverse Correspondences over Inverse Semigroups

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Tomoki Uchimura

摘要

We introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert C*-modules and C*-correspondences in the theory of C*-algebras. 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.