AbstractWe study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite-dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by Kazhdan–Lusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do not depend on the choice of a right cell inside a two-sided cell. This reproves and extends the

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... uniqueness result on categorification of Kazhdan–Lusztig cell modules for Hecke algebras of typeAfrom [V. Mazorchuk and C. Stroppel,Categorification of (induced) cell modules and the rough structure of generalised Verma modules, Adv. Math. 219(2008), 1363–1426].