2-Representations of simple Lie algebras are expected to lead to 4-dimensional TQFTs, as envisioned by Crane and Frenkel. The tensor product of 2-representations introduces homotopical phenomena which disappear when considering instead the case of the super Lie algebra gl(1|1). I will discuss how to construct parts of the structure of a braided monoidal 2-category associated to gl(1|1), and how this compares with the known 4-dimensional Heegaard–Floer TQFT.