Braided vector space
In mathematics, a braided vector space V {\displaystyle \;V} is a vector space together with an additional structure map τ {\displaystyle \tau } symbolizing interchanging of two vector tensor copies: τ : V ⊗ V ⟶ V ⊗ V {\displaystyle \tau :\;V\otimes V\longrightarrow V\otimes V} such that the Yang–Baxter equation is fulfilled. Hence drawing tensor diagrams with τ {\displaystyle \tau } an overcrossing the corresponding composed morphism is unchanged when a Reidemeister move is applied to the tensor diagram and thus they present a representation of the braid group.