Abstract:
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Given a pseudomonad T, we prove that a lax T-morphism between pseudoalgebras is a T-pseudomorphism if and only if there is a suitable (possibly non-canonical) invertible T-transformation. This result encompasses several results on non-canonical isomorphisms, including Lack's result on normal monoidal functors between braided monoidal categories, since it is applicable in any 2-category of pseudoalgebras, such as the 2-categories of monoidal categories, cocomplete categories, pseudofunctors and so on. |