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The geometry of Coherent topoi and Ultrastructures

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arxiv 2211.03104 v1 pith:Z2EKU3KM submitted 2022-11-06 math.CT math.GNmath.LO

Ivan Di Liberti This is my paper · ORCID
classification math.CTmath.GNmath.LO
keywords topoicoherentarenascategoryconsequenceembeddingsflatformal
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We show that coherent topoi are right Kan injective with respect to flat embeddings of topoi. We recover the ultrastructure on their category of points as a consequence of this result. We speculate on possible notions of ultracategory in various arenas of formal model theory.

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Cited by 2 Pith papers

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.

  2. Ultracategories via Kan extensions of relative monads

    math.CT 2025-06 conditional novelty 7.0 of 10

    Left oplax Kan extensions turn relative 2-monads into pseudomonads with the same colax algebras, producing the weak ultracompletion pseudomonad for ultracategories.

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