Braided tensor categories and extensions of vertex operator algebras
  Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions of extension (i.e., enlargement) of $V$ and of commutative associative algebra, with uniqueness of unit and with trivial twist, in the braided tensor category of $V$-modules are equivalent. 
Yi-Zhi Huang, Alexander Kirillov Jr. and James Lepowsky
math.QA hep-th math.RT