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Pseudogroups and their torsors

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Abstract

We provide a close analysis of the connections between pseudogroups, groupoids, and toposes. This analysis provides a topos perspective on both the localic germ groupoid of a pseudogroup defined by Resende, and the topological groupoid of a pseudogroup defined by Lawson and Lenz. In particular, we show how to analyze the topos of a pseudogroup using sheaf theory, leading to an examination of pseudogroup torsors. Consequently we obtain a concrete description of the category of points of an étendue.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Jonathon Funk

  2. CUNY Queensborough Community College, Bayside, NY, USA

    Pieter Hofstra

Authors
  1. Jonathon Funk
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  2. Pieter Hofstra
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Correspondence to Pieter Hofstra.

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Communicated by Mark V. Lawson.

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Funk, J., Hofstra, P. Pseudogroups and their torsors. Semigroup Forum 104, 281–319 (2022). https://doi.org/10.1007/s00233-022-10261-x

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  • DOI: https://doi.org/10.1007/s00233-022-10261-x

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