Ultracategories as colax algebras for a pseudo-monad on CAT

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

Publication Details

Journal
ArXiv.org
Published
2025-02-27
Primary Topic
Homotopy and Cohomology in Algebraic Topology
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article
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article

Ultracategories as colax algebras for a pseudo-monad on CAT

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

Ultracategories as colax algebras for a pseudo-monad on CAT

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Abstract

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

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 45%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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Ultracategories as colax algebras for a pseudo-monad on CAT · ArXiv.org (2025) | TGRS Research Map | TGRS