Name passing calculi are nowadays one of the preferred formalisms for the specification of concurrent and distributed systems with a dynamically evolving topology. Despite their widespread adoption as a theoretical tool, though, they still face some unresolved semantic issues, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully employed for languages with symmetric communication, like the π -calculus, are presheaf categories based on injective) relabellings, such as Set^I . Calculi with symmetric binding, in the spirit of the fusion calculus, give rise to novel research challenges. In this work we examine the explicit fusion calculus, and propose to model its syntax and semantics using the presheaf category Set^E , where E is the category of equivalence relations and equivalence preserving morphisms.