Ultracategories as colax algebras for a pseudo-monad on CAT

Ali Hamad

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arXiv · 2502.20597

Ultracategories as colax algebras for a pseudo-monad on CAT

Ali Hamad

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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.

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Ali Hamad. 2025-02-27. Ultracategories as colax algebras for a pseudo-monad on CAT. https://arxiv.org/abs/2502.20597

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