I will discuss recent work with Raphael Rouquier, focusing on a higher tensor product operation for 2-representations of Khovanov's categorification of U(gl(1|1)^+), examples of such 2-representations that arise as strands algebras in bordered and cornered Heegaard Floer homology, and a tensor-product-based gluing formula for these 2-representations expanding on work of Douglas-Manolescu.