Abstract

We prove a topological version of abelian duality where the gauge groups are finite abelian. The theories are finite homotopy TFTs, topological analogues of the p-form U(1) gauge theories and a generalization of abelian Dijkgraaf-Witten theories. We extend such duality to a subset of higher-group symmetries, which goes by the name of π-finite spectra. Furthermore, I will discuss the relation between this duality and gauging/ungauging in 2, 3 dimensions.