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Pseudoalgebras and Non-canonical Isomorphisms

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Abstract

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.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, Portugal

    Fernando Lucatelli Nunes

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  1. Fernando Lucatelli Nunes
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Correspondence to Fernando Lucatelli Nunes.

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Communicated by Nicola Gambino.

Research partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.

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Lucatelli Nunes, F. Pseudoalgebras and Non-canonical Isomorphisms. Appl Categor Struct 27, 55–63 (2019). https://doi.org/10.1007/s10485-018-9541-3

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  • DOI: https://doi.org/10.1007/s10485-018-9541-3

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