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Ultracategories as colax algebras for a pseudo-monad on CAT

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arxiv 2502.20597 v3 pith:YZDA372M submitted 2025-02-27 math.CT

Ali Hamad This is my paper · ORCID
classification math.CT
keywords algebrascolaxdefinedluriepseudo-monadultracategoriesallowscategories
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We show a result inspired by a conjecture by Shulman claiming that ultracategories as defined by Lurie are normal colax algebras for a certain pseudo-monad on the category of categories CAT. Such definition allows us to regard left and right ultrafunctors as defined by Lurie as instances of lax/colax algebras morphisms

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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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