Hi, This question came up to me when reading the paper of Cartier on Vassiliev invariants, but it can probably be turned into a more general question. Let $T$ be the category who …

So, there's a construction of Reshetikhin and Turaev which extracts knot invariants from ribbon monoidal categories, which are (usually) the representation category a Hopf algebra …

I'm just going assume readers are familiar with the notions of R-matrix and ribbon categories. Given a quasi-triangular Hopf algebra $A$ with $R$-matrix $R$, one can construct the …