Suppose $H$ is a cocommutative Hopf algebra in a braided monoidal category$C$ and suppose $H$ acts on another Hopf algebra $B$ in $C$. Then a smash product and smash coproduct of the two has a structure of an ordinary Hopf algebra called a Radford biproduct or Majid bosonisation of $H$. In an intuitive description, it turns the braided statistics into a bosonic statistics. A particular case is the case of super-Hopf algebras related to the more traditional physical concept of bosonization.

Majid uses English spelling bosonisation rather than bosonization, so it is a tradition that the following literature uses the same spelling for the algebraic concept.