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Operational congruences for reactive systems
, 2001
"... This document consists of a slightly revised and corrected version of a dissertation ..."
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Cited by 35 (4 self)
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This document consists of a slightly revised and corrected version of a dissertation
Paracategories I: Internal Paracategories and Saturated Partial Algebras
 Comp. Sci
, 2002
"... Based on the monoid classi er , we give an alternative axiomatization of Freyd's paracategories, which can be interpreted in any bicategory of partial maps. Assuming furthermore a freemonoid monad T in our ambient category, and coequalisers satisfying some exactness conditions, we give an ..."
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Cited by 5 (1 self)
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Based on the monoid classi er , we give an alternative axiomatization of Freyd's paracategories, which can be interpreted in any bicategory of partial maps. Assuming furthermore a freemonoid monad T in our ambient category, and coequalisers satisfying some exactness conditions, we give an abstract envelope construction, putting paramonoids (and paracategories) in the more general context of partial algebras . We introduce for the latter the crucial notion of saturation, which characterises those partial algebras which are isomorphic to the ones obtained from their enveloping algebras. We also set up a factorisation system for partial algebras, via inclusions and Kleene morphisms.
Monads on Composition Graphs
 UNIVERSITY OF BREMEN
, 2000
"... Collections of objects and morphisms that fail to form categories inasmuch as the expected composites of two morphisms need not always be defined have been introduced in [14, 15] under the name composition graphs. In [14, 16], notions of adjunction and weak adjunction for composition graphs have bee ..."
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Collections of objects and morphisms that fail to form categories inasmuch as the expected composites of two morphisms need not always be defined have been introduced in [14, 15] under the name composition graphs. In [14, 16], notions of adjunction and weak adjunction for composition graphs have been proposed. Building on these definitions, we now introduce a concept of monads for composition graphs and show that the usual correspondence between adjunctions and monads remains correct, i.e. that (weak) adjunctions give rise to monads and that all monads are induced by adjunctions. Monads are described in terms of natural transforms as well as in terms of Kleisli triples, which seem to be better suited in the absence of associativity. The realization of a monad by an adjunction relies on a generalization of the Kleisli construction to composition graphs; on the other hand, the EilenbergMoore construction produces only a weak adjunction and admits comparison functors from weak adjuncti...
INTERCONNECTION OF PROBABILISTIC SYSTEMS
, 2000
"... There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of ..."
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Cited by 3 (3 self)
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There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of
Realization of Probabilistic Automata: Categorical Approach
 Recent Developments in Algebraic Development Techniques  Selected Papers, volume 1827 of Lecture Notes in Computer Science. SpringerVerlag. In print
"... . We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we ..."
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. We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we are able to extend to the probabilistic setting free and minimal realizations as universal constructions. 1 Introduction Probabilistic automata [Rab63,Paz66] are central in the theory of unreliable systems, namely for providing the appropriate semantic domain (see for instance [BDEP97,LS91,vGSST95]). In particular we adopt the Moore model, that is, the outputs are assigned to the states. In [MSS99,SM99] we provided a (pre)categorical characterization for several combinations of probabilistic automata. However, we had to work with structures weaker than categories [Ehr65,Cop80] because composition of morphisms was not always dened. Herein we adopt a dierent approach by considering that th...
Paracategories II: Adjunctions, fibrations and examples from probabilistic automata theory
, 2002
"... In this sequel to [HM02], we explore some of the global aspects of the category of paracategories. We establish its (co)completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We setup the relevant notion of adjunction betwee ..."
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In this sequel to [HM02], we explore some of the global aspects of the category of paracategories. We establish its (co)completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We setup the relevant notion of adjunction between paracategories and apply it to define (co)completeness and cartesian closure, exemplified by the paracategory of bivariant functors and dinatural transformations. We introduce partial multicategories to account for partial tensor products. We also consider fibrations for paracategories and their indexedparacategory version. Finally, we instantiate all these concepts in the context of probabilistic automata.
Internal Paracategories
, 2000
"... Based on the monoid classi er , we give an alternative axiomatization of Freyd's paracategories. This abstract reformulation can be interpreted in any category which admits the construction of a bicategory of partial maps. Assuming furthermore a free monoid monad T in our ambient category, ..."
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Based on the monoid classi er , we give an alternative axiomatization of Freyd's paracategories. This abstract reformulation can be interpreted in any category which admits the construction of a bicategory of partial maps. Assuming furthermore a free monoid monad T in our ambient category, and coequalisers satisfying some exactness conditions, we give an abstract envelope construction, and put paramonoids (and paracategories) in the more general context of partial algebras. We then consider the cartesian closed structure of the category of paracategories and the relevant notion of adjunction in the enriched context which ensues. We conclude by presenting in this framework some ( bred) paracategories which arise in the theory of probabilistic automata.