# Pseudoalgebras and Non-canonical Isomorphisms

@article{LucatelliNunes2018PseudoalgebrasAN,
title={Pseudoalgebras and Non-canonical Isomorphisms},
author={Fernando Lucatelli Nunes},
journal={Applied Categorical Structures},
year={2018},
volume={27},
pages={55-63}
}
Given a pseudomonad $$\mathcal {T}$$T, we prove that a lax $$\mathcal {T}$$T-morphism between pseudoalgebras is a $$\mathcal {T}$$T-pseudomorphism if and only if there is a suitable (possibly non-canonical) invertible $$\mathcal {T}$$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…
1 Citations
• Mathematics
Journal of Pure and Applied Algebra
• 2022

## References

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Abstract The formal theory of monads can be developed in any 2-category, but when it comes to pseudomonads, one is forced to move from 2-categories to Gray-categories (semistrict 3-categories). The