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

@article{Mackaay2016SimpleT2,
  title={Simple transitive 2-representations via (co)algebra 1-morphisms},
  author={Marco Mackaay and Volodymyr Mazorchuk and Vanessa Miemietz and Daniel Tubbenhauer},
  journal={Indiana University Mathematics Journal},
  year={2016}
}
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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