• DOI:10.1007/s10485-018-9541-3
• Corpus ID: 195217682

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}
}

• Fernando Lucatelli Nunes
• Published 15 September 2018
• Mathematics
• Applied Categorical Structures

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 monoidal categories, cocomplete categories, bicategories, pseudofunctors and so on.