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Duke Math. Jour. 47 (1980), 1–15. J. Fischer. 2-categories and 2-knots. Duke Math J. 75 (1994), 493–526. B. Frenkel and M. Khovanov. Canonical bases in tensor products and graphical calculus for Uq (sl2 ). Duke Math J. 87 (1997), 409–480. B. Frenkel, M. Khovanov and A. Kirillov, Jr. Kazhdan-Lusztig polynomials and canonical basis. Transformation Groups 3 (1998), 321–336. K. M. Green. Monomials and Temperley-Lieb algebras. J. Algebra 190 (1997), 498–517. B. Frenkel and F. Malikov. Annihilating ideals and tilting functors.

The composition Γ1i εi−1 Γ1i−1 εi is isomorphic to the identity functor i from the category Ok,n−k to itself. Proof. By Lemma 2 it remains to show that functors Γ1i−1 εi and Γ1i εi−1 are twoi is right adjoint to the inclusion sided adjoint. We recall that Γi : Ok,n−k → Ok,n−k functor εi . Besides, in the derived category, the derived functor RΓi is isomorphic to the left adjoint of the shifted inclusion functor εi [2]. Vol. 5 (1999) Categorification of Temperley-Lieb algebra 229 i Let M, N ∈ Ok,n−k .