Given a Hopf algebra H and a Yetter–Drinfeld module V over H, it is well-known that V has an induced braided vector space structure, and so, one can consider it’s Nichols algebra which is a braided Hopf algebra in the braided monoidal category of Yetter–Drinfeld modules over H.

The notion, however, of a Nichols algebra makes sense for any object in any braided monoidal category C. Is it true in general that the Nichols algebra of any object in C will be a braided Hopf algebra in C?

**Answer**

**Attribution***Source : Link , Question Author : Abo Kutis-Felan , Answer Author : Community*