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On topological groupoids that represent theories

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arxiv 2306.16331 v2 pith:W3PAOKNK submitted 2023-06-28 math.CT math.AGmath.LO

classification math.CTmath.AGmath.LO
keywords topologicalgroupoidstoposbutzenoughmoerdijkopenrepresent
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Grothendieck toposes, and by extension, logical theories, can be represented by topological structures. Butz and Moerdijk showed that every topos with enough points can be represented as the topos of sheaves on an open topological groupoid. This paper tackles a follow-up question: we characterise, in model-theoretic terms, which open topological groupoids can represent the classifying topos of a theory. Intuitively, this characterises which groupoids of models contain enough information to reconstruct the theory. Our treatment subsumes many of the previous approaches found in the literature, such as that of Awodey, Forssell, Butz and Moerdijk.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Extending conceptual completeness via virtual ultracategories

    math.CT 2025-06 reject novelty 7.0 of 10

    It defines virtual ultracategories and claims every Grothendieck topos with enough points is equivalent to the category of ultrasheaves on the virtual ultracategory of its points.

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