Name-passing calculi are specification languages for concurrent
systems, considered as structured entities interacting via some kind
of synchronisation mechanism.  One of the main challenges for such
languages has been represented by the development of adequate
denotational semantics. Only recently the use of presheaf categories
proved fruitful for providing fully abstract models to those calculi
with a symmetric communication mechanism, like the $\pi$-calculus.
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 The index categories which have been successfully employed for such
 languages are based on (injective) name relabellings, resulting e.g.
 in the presheaf category $\Set^{\mathbb{I}}$, for $\mathbb{I}$ the category of
 (finite) sets and injective functions.

 In this talk we consider a calculus based on a different
 synchronisation mechanism: the \emph{calculus of explicit fusions},
 where process communication relies on an underlying store of name
 equalities. We propose to model both its syntax and semantics using
 the presheaf category $\Set^{\mathbb{E}}$: each object of
 $\mathbb{E}$ is an equivalence relation over a (finite) set of names and,
 analogously to $\mathbb{I}$, morphisms preserve names,
% (i.e., names can not be junked away),
 but equivalence classes can be merged,
 thus obtaining semantical fusion of names without loosing any
 syntactical name.
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 Besides recasting coalgebraically the standard semantics for
 explicit fusions, the so-called \emph{inside-outside bisimulation},
 we furthermore investigate the connections between $\Set^\I$ and
 $\Set^\E$, trying to highlight some correspondences between the
 languages themselves.