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