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arXiv · 1711.02051

Pseudoalgebras and non-canonical isomorphisms

Fernando Lucatelli Nunes
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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 \textit{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.

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Fernando Lucatelli Nunes. 2018-08-24. Pseudoalgebras and non-canonical isomorphisms. https://doi.org/10.1007/s10485-018-9541-3

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