The goal of the talk is to introduce the symmetric monoidal (infty,2)-category Gr of finite sets, graph cobordisms, and tree collapse maps, and to state its universal property as a free symmetric monoidal extension of finite sets with disjoint union. As an application we will recover a result originally due to Barkan and Steinebrunner, exhibiting the localisation of GR at all 2-morphisms as the symmetric monoidal (infty,1)-category freely generated by an E_infty Frobenius algebra.