Mackaay, MarcoMazorchuk, VolodymyrMiemietz, VanessaTubbenhauer, Daniel2020-07-242020-07-2420190022-25181943-5258http://hdl.handle.net/10400.1/14484For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 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, including that of Soergel bimodules for dihedral groups, explicitly.engHopf-AlgebrasCategoriesBimodulesSimple transitive 2-representations via (Co-)Algebra 1-Morphismsjournal article10.1512/iumj.2019.68.7554