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arXiv · 2506.09788

Ultracategories via Kan extensions of relative monads

Umberto Tarantino·Joshua Wrigley
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Abstract

Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad.

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Umberto Tarantino, Joshua Wrigley. 2025-06-11. Ultracategories via Kan extensions of relative monads. https://arxiv.org/abs/2506.09788

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