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

Abstract

For any fiat 2-category C, we show how its simple transitive\n2-representations can be constructed using coalgebra 1-morphisms in the\ninjective abelianization of C. Dually, we show that these can also be\nconstructed using algebra 1-morphisms in the projective abelianization of C. We\nalso extend Morita-Takeuchi theory to our setup and work out several examples\nexplicitly.\n