ИСТИНА

A braided set is the same as a solution of the set-theoretic Yang-Baxter equation, which allows generalization in a categorical language. I will talk about several central aspects in constructing the category of branded sets, including approaches to determine extensions of such objects. This question is directly related to the natural constructions of the quantum inverse scattering method, in particular with the construction of the Drinfeld double. In addition, I will talk about possible generalizations for the case of higher dimensions, that is, for the case of 2-tangles.