Applied Categorical Structures

, Volume 27, Issue 1, pp 55–63 | Cite as

Pseudoalgebras and Non-canonical Isomorphisms

  • Fernando Lucatelli NunesEmail author


Given a pseudomonad \(\mathcal {T}\), we prove that a lax \(\mathcal {T}\)-morphism between pseudoalgebras is a \(\mathcal {T}\)-pseudomorphism if and only if there is a suitable (possibly non-canonical) invertible \(\mathcal {T}\)-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, bicategories, pseudofunctors and so on.


Pseudomonads Lax morphisms Monoidal functors Braided monoidal categories Canonical morphisms Two-dimensional monad theory 

Mathematics Subject Classification

18D05 18C15 18C20 18D10 


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal

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