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Coalgebra Morphisms Subsume Open Maps
, 1999
"... We relate two abstract notions of bisimulation, induced by open maps and by coalgebras morphisms, respectively. We show that open maps correspond to coalgebra morphisms for a suitable chosen endofunctor in a category of many sorted sets. This demonstrates that the notion of openmaps bisimilarity is ..."
Abstract

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We relate two abstract notions of bisimulation, induced by open maps and by coalgebras morphisms, respectively. We show that open maps correspond to coalgebra morphisms for a suitable chosen endofunctor in a category of many sorted sets. This demonstrates that the notion of openmaps bisimilarity is of essentially coalgebraic nature. We nd moreover characterizations of subcategories of coalgebras corresponding to some relevant model categories: category of presheaves is isomorphic to the subcategory of consistent coalgebras with lax cohomomorphisms; a suitably chosen subcategory of many sorted algebras is equivalent to the full subcategory of presheaves preserving nite products.
PartialCongruence Factorization of Bisimilarity Induced by Open Maps
 Proc. 25th ICALP, Aalborg, LNCS 1443 (SpringerVerlag
, 1998
"... We investigate relationships between bisimilarity defined by open maps and behavioural equivalence factorized by indistinguishability relations. This is done in the setting of a concrete category supporting algebraic constructions of subobject and quotient. Under some mild assumptions, a sufficient ..."
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We investigate relationships between bisimilarity defined by open maps and behavioural equivalence factorized by indistinguishability relations. This is done in the setting of a concrete category supporting algebraic constructions of subobject and quotient. Under some mild assumptions, a sufficient condition is found for bisimilarity to be factorizable by the greatest open congruences. Moreover, we find a necessary and sufficient condition for a factorization of bisimilarity: it is factorizable iff quotients by all maximal open congruences are isomorphic. The general results are motivated and illustrated by important examples: transition systems, event structures and presheaf models.
Weak Bisimilarity and Open Maps
"... An alternative proof (to that from [3]) is presented for weak bisimilarity of transition systems to be abstractly definable by open maps [9]. This result arises from an observation that the categories (of transition systems) well suited for studying strong and weak bisimulations are related by an ad ..."
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An alternative proof (to that from [3]) is presented for weak bisimilarity of transition systems to be abstractly definable by open maps [9]. This result arises from an observation that the categories (of transition systems) well suited for studying strong and weak bisimulations are related by an adjunction (for a suitable monad), giving a link between both bisimilarities. We formulate a generalization of this result, hopefully applicable also to other equivalences of processes.