Narrow Results

Generalized Temperley–Lieb–Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong ∗-pseudofunctors into the ∗-2-category of row-finite separable bigraded Hilbert spaces. We classify these modules up to ∗-equivalence in terms of weighted bi-directed fair and balanced graphs in the spirit of Yamagami’s classification of fiber functors on TLJ categories and DeCommer and Yamashita’s classification of unitary modules for ${\mathrm{\text{Rep(SU}}}_q(2))$.