Morita equivalence of pseudogroups

M. V. Lawson, P. Resende

Research output: Contribution to journalArticlepeer-review

Abstract

We take advantage of the correspondence between pseudogroups and inverse quantal frames, and of the recent description of Morita equivalence for inverse quantal frames in terms of biprincipal bisheaves, to define Morita equivalence for pseudogroups and to investigate its applications. In particular, two pseudogroups are Morita equivalent if and only if their corresponding localic étale groupoids are. We explore the clear analogies between our definition of Morita equivalence for pseudogroups and the usual notion of strong Morita equivalence for C-algebras and these lead to a number of concrete results.

Original languageEnglish
Pages (from-to)718-755
Number of pages38
JournalJournal of Algebra
Volume586
Early online date21 Jul 2021
DOIs
Publication statusE-pub ahead of print - 21 Jul 2021

Keywords

  • Inverse quantal frames
  • Inverse semigroups
  • Morita equivalence
  • Pseudogroups
  • Quantales
  • Étale groupoids

ASJC Scopus subject areas

  • Algebra and Number Theory

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