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In Lack's A 2-categories companion, he states There are general results asserting that any bicategory is biequivalent to a 2-category, but in fact naturally occurring bicategories tend to be ...

For every pseudomonad $T$ on the 2-category of (locally small) categories $\mathbf{Cat}$, we can consider the 2-category of $T$-pseudoalgebras and pseudomorphisms $T\text{-PsAlg}_p$, which is equipped ...