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A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 28 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
Notes on enriched categories with colimits of some class
 Theory Appl. Categ
"... The paper is in essence a survey of categories having φweighted colimits for all the weights φ in some class Φ. We introduce the class Φ + of Φflat weights which are those ψ for which ψcolimits commute in the base V with limits having weights in Φ; and the class Φ − of Φatomic weights, which are ..."
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Cited by 9 (0 self)
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The paper is in essence a survey of categories having φweighted colimits for all the weights φ in some class Φ. We introduce the class Φ + of Φflat weights which are those ψ for which ψcolimits commute in the base V with limits having weights in Φ; and the class Φ − of Φatomic weights, which are those ψ for which ψlimits commute in the base V with colimits having weights in Φ. We show that both these classes are saturated (that is, what was called closed in the terminology of [AK88]). We prove that for the class P of all weights, the classes P + and P − both coincide with the class Q of absolute weights. For any class Φ and any category A, we have the free Φcocompletion Φ(A) of A; and we recognize Q(A) as the Cauchycompletion of A. We study the equivalence between (Q(A op)) op and Q(A), which we exhibit as the restriction of the Isbell adjunction between [A, V] op and [A op, V] when A is small; and we give a new Morita theorem for any class Φ containing Q. We end with the study of Φcontinuous weights and their relation to the Φflat weights. 1
Polycategories via pseudodistributive laws
"... In this paper, we give a novel abstract description of Szabo’s polycategories. We use the theory of double clubs – a generalisation of Kelly’s theory of clubs to ‘pseudo ’ (or ‘weak’) double categories – to construct a pseudodistributive law of the free symmetric strict monoidal category pseudocomo ..."
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Cited by 7 (1 self)
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In this paper, we give a novel abstract description of Szabo’s polycategories. We use the theory of double clubs – a generalisation of Kelly’s theory of clubs to ‘pseudo ’ (or ‘weak’) double categories – to construct a pseudodistributive law of the free symmetric strict monoidal category pseudocomonad on Mod over itself qua pseudomonad, and show that monads in the ‘twosided Kleisli bicategory’ of this pseudodistributive law are precisely symmetric polycategories. 1
On Braidings, Syllepses, and Symmetries
, 1998
"... this paper is that these are the only differences between (semistrict) braided monoidal 2categories (as defined in [10]) and braided 2D teisi. The interpretation of this is that the main obstacles for proving the conjecture above will be the weakness of functoriality and the weakness of invertibili ..."
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this paper is that these are the only differences between (semistrict) braided monoidal 2categories (as defined in [10]) and braided 2D teisi. The interpretation of this is that the main obstacles for proving the conjecture above will be the weakness of functoriality and the weakness of invertibility. I should mention here that Baez and Neuchl [5, p. 242] (as corrected by me [10, p. 206]) have shown that either one of the functoriality triangles above can be made into an identity, but it is essential to the proof that the other one is not. Defining monoidal 2D teisi as 3D teisi with one object involves a shift of dimension: the arrows, 2arrows and 3arrows of the 3D tas C become the objects, arrows and 2arrows of a 2D tas which will be called the looping of
Tannaka Reconstruction for Crossed Hopf Group Algebras
, 2008
"... We provide an analog of Tannaka Theory for Hopf algebras in the context of crossed Hopf group coalgebras introduced by Turaev. Following Street and our previous work on the quantum double of crossed structures, we give a construction, via Tannaka Theory, of the quantum double of crossed ..."
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We provide an analog of Tannaka Theory for Hopf algebras in the context of crossed Hopf group coalgebras introduced by Turaev. Following Street and our previous work on the quantum double of crossed structures, we give a construction, via Tannaka Theory, of the quantum double of crossed
Bisimulation of enrichments
, 2006
"... In this paper we show that classical notions from automata theory such as simulation and bisimulation can be lifted to the context of enriched categories. The usual properties of bisimulation are nearly all preserved in this new context. The class of enriched functors that correspond to functionnal ..."
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In this paper we show that classical notions from automata theory such as simulation and bisimulation can be lifted to the context of enriched categories. The usual properties of bisimulation are nearly all preserved in this new context. The class of enriched functors that correspond to functionnal bisimulations surjective on objects is investigated and appears to be “very close ” to be open in the sense of Joyal and Moerdijk [4]. Seeing the change of base techniques as a convenient means to define process refinement/abstractions we give sufficient conditions for the change of base categories to preserve bisimularity. We apply these concepts to Betti’s generalized automata, categorical transition systems, and other exotic categories. 1