  We analyze the non-semisimple category of line operators in Chern-Simons
gauge theories based off the Lie superalgebra $\mathfrak{gl}(1|1)$. Our
proposal is that the category of line operators $\mathcal{C}$ can be identified
with the derived category of modules for a boundary vertex operator algebra
$\mathcal{V}$ realized as a certain infinite-order simple current extension of
the affine current algebra $V(\mathfrak{gl}(1|1))$ by boundary monopole
operators. By translating this simple current extension of
$V(\mathfrak{gl}(1|1))$ to the unrolled, restricted quantum group
${\overline{U}}^E(\mathfrak{gl}(1|1))$, we show that our category of line
operators admits a second description in terms of a quantum group $\mathcal{A}$
realized by uprolling. We also compare our results across an expected physical
duality with the cyclic orbifold of a free, $B$-twisted hypermultiplet and find
a slight discrepancy at the level of braiding. We end with a detailed analysis
of coupling to background flat $GL(1, \mathbb{C})$ connections and the
resulting category of non-genuine line operators.
