  We study the simplest example of mirror symmetry for 3d $\mathcal N=4$ SUSY
gauge theories: the A-twist of a free hypermultiplet and the B-twist of SQED.
We particularly focus on the category of line operators in each theory. Using
the work of Costello-Gaiotto, we define these categories as appropriate
categories of modules for the boundary vertex operator algebras present in each
theory. For the A-twist of a free hyper, this will be a certain category of
modules for the $\beta\gamma$ VOA, properly containing the category previously
studied by Allen-Wood. Applying the work of Creutzig-Kanade-McRae and
Creutzig-McRae-Yang, we show that the category of line operators on the A side
possesses the structure of a braided tensor category, extending the result of
Allen-Wood. In addition, we prove that there is a braided tensor equivalence
between the categories of line operators on the A side and B side, completing a
non-trivial check of the 3d mirror symmetry conjecture. We derive explicit
fusion rules as a consequence of this equivalence and obtain interesting
relations with associated quantum group representations.
