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- W4301293669 abstract "We describe a finitary 2-monad on a locally finitely presentable 2-category for which not every pseudoalgebra is equivalent to a strict one. This shows that having rank is not a sufficient condition on a 2-monad for every pseudoalgebra to be strictifiable. Our counterexample comes from higher category theory: the strict algebras are strict 3-categories, and the pseudoalgebras are a type of semi-strict 3-category lying in between Gray-categories and tricategories. Thus, the result follows from the fact that not every Gray-category is equivalent to a strict 3-category, connecting 2-categorical and higher-categorical coherence theory. In particular, any nontrivially braided monoidal category gives an example of a pseudoalgebra that is not equivalent to a strict one." @default.
- W4301293669 created "2022-10-05" @default.
- W4301293669 creator A5065839536 @default.
- W4301293669 date "2010-05-10" @default.
- W4301293669 modified "2023-10-16" @default.
- W4301293669 title "Not every pseudoalgebra is equivalent to a strict one" @default.
- W4301293669 doi "https://doi.org/10.48550/arxiv.1005.1520" @default.
- W4301293669 hasPublicationYear "2010" @default.
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