What is this sophistication thing anyway?

Abstract Following Dewar (2019), ‘reduction’ and ‘sophistication’ are supposed to be two different ways of articulating the shared content of symmetry-related models of physical theories. And yet: there does not exist in the literature a maximally clear, maximally general statement as to what the distinction between reduction and sophistication amounts to. In this article, we present a proposal in order to redress this issue: the proposal is to understand reduction and sophistication not as intrinsic properties of physical theories, but rather as four-place relations between two theories, a map between those theories, and a set of symmetries of the former theory. We go on to extol various virtues of this way of thinking about the reduction/sophistication distinction.