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arXiv · 1612.06325

Simple transitive 2-representations via (co)algebra 1-morphisms

Marco Mackaay·Volodymyr Mazorchuk·Vanessa Miemietz·Daniel Tubbenhauer
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Abstract

For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples explicitly.

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Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz, Daniel Tubbenhauer. 2019-02-06. Simple transitive 2-representations via (co)algebra 1-morphisms. https://doi.org/10.1512/iumj.2019.68.7554

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