A bicategorical generalization of monad extensions to profunctors yields a characterization of ultraconvergence spaces as normalized lax algebras of the ultracompletion pseudomonad.
Coherence and normalisation-by-evaluation for bicategorical cartesian closed structure
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Profunctorial algebras
A bicategorical generalization of monad extensions to profunctors yields a characterization of ultraconvergence spaces as normalized lax algebras of the ultracompletion pseudomonad.