This is a report of work in progress. On the one hand, based on an article by R. Borcherds, but also of previous authors, I presented in a recent manuscript a description of the renormalisation procedure of perturbative quantum field theory (pQFT). This made use of several algebraic constructions from higher category theory, in particular, 2-monoidal categories, which are in particular suitable to deal with the relation between composite fields and time-ordered products. The constructions remain however highly involved and hard to grasp. On the other hand, in an attempt to make the theory of vertex algebras more natural, Borcherds also proposed a new foundation based on two tensor products. In this talk I will explain how these ideas sit well within the framework of 2-monoidal categories with the aim of also encompassing the description of pQFT mentioned previously.