A braided object in a monoidal category is an object equipped with an invertible morphism satisfying the Yang-Baxter equation
More generally, if is not necessarily invertible but still satisfies the Yang-Baxter equation, then is called a pre-braided object.
Victoria Lebed, Objets tressés: une étude unificatrice de structures algébriques et une catégorification des tresses virtuelles, Thèse, Université Paris Diderot, 2012. (pdf) Note that the title is in French (“Braided objects: a unifying study of algebraic structures and a categorification of virtual braids”) but the main text of the thesis is in English.
Victoria Lebed, Categorical Aspects of Virtuality and Self-Distributivity, Journal of Knot Theory and its Ramifications, 22 (2013), no. 9, 1350045, 32 pp. (doi) According to the author, arXiv:1206.3916 is “an extended version of the above JKTR publication, containing in particular a chapter on free virtual shelves and quandles”.
Created on December 22, 2016 at 15:00:59. See the history of this page for a list of all contributions to it.