We are interested in providing a categorical framework (and denotational semantics) for certain "light" linear logics. These include Bounded, Soft, Light and Elementary linear logics, for example. In this talk we shall focus on Soft linear logic and give a categorical interpretation in terms of "multiplexor categories". We shall describe a categorical construction for building a multiplexor category from a suitable categorical model of a simplified version of Bounded linear logic. We shall see how this is related to recent work by Olivier Laurent and Lorenzo Tortora de Falco on Obsessional cliques, as well as to my recent work on realizability models for Soft linear logic.