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

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.

Revised version to appear in Indiana Univ. Math. J. the numbering of theorems etc. is changed to adjust to the published version

References in corpus (2)

• Derived equivalences for symmetric groups and sl\_2-categorification
• Duflo involutions for 2-categories associated to tree quivers

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• 2-categories of symmetric bimodules and their 2-representations
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• Coidempotent subcoalgebras and short exact sequences of finitary 2-representations
• 2-representations of small quotients of Soergel bimodules in infinite types
• Adjunction in the absence of identity
• Sub-bimodules of the identity bimodule for cyclic quivers
• Classification problems in 2-representation theory