3 problems

Let $K\subset S^3$ be a framed oriented knot and let $X\in\operatorname{Ch}^-(\mathsf{BN}_n)$ be a complex of $n$-strand Bar–Natan 1-morphisms. Let $C(K,V_n)$ denote the $V_n$-colo…

Let $K$ be a framed oriented knot, let $\operatorname{Kar}(\mathcal T\mkern-3mu\mathcal L)^\oplus$ be the additive Karoubi envelope of the Temperley–Lieb category, and let $V_n$ de…

Let $\kappa$ be the coefficient field, let $\operatorname{Ch}^-(\mathsf{BN}_n)$ be the homotopy category of bounded-above complexes of $n$-strand Bar–Natan 1-morphisms, and let…