## A categorical model of the fusion calculus

Dipartimento di Matematica e Informatica

Università degli Studi di Udine

Thursday, 11 February 2010, 14:00

Cybernetica Bldg (Akadeemia tee 21), room B101

Slides from the talk [pdf]

**Abstract**: We provide a categorical presentation of the
fusion calculus. Working in a suitable category of presheaves, we
describe the syntax as initial algebra of a signature endofunctor, and
the semantics as coalgebras of a "behaviour" endofunctor. To this end,
we first give a a new, congruence-free presentation of the Fusion
calculus; then, the behaviour endofunctor is constructed by adding in
a systematic way a notion of "state" to the intuitive endofunctor
induced by the LTS. Coalgebras can be given a concrete presentation as
"stateful indexed labelled transition systems"; the bisimilarity over
these systems is a congruence, and corresponds to
hyperequivalence. Then, we model the labelled transition system of the
fusion calculus by abstract categorical rules. As a consequence, we get a
semantics for the fusion calculus which is both compositional and
fully abstract: two processes have the same semantics if they are
bisimilar, that is, hyperequivalent.

Tarmo Uustalu

Last update 11 February 2010