  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.
