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101
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Cited by 12 (3 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
The Convergence Approach to Exponentiable Maps
 352 MARIA MANUEL CLEMENTINO, DIRK HOFMANN AND WALTER
, 2000
"... Exponentiable maps in the category Top of topological spaces are characterized by an easy ultrafilterinterpolation property, in generalization of a recent result by Pisani for spaces. From this characterization we deduce that perfect (= proper and separated) maps are exponentiable, generalizing the ..."
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Exponentiable maps in the category Top of topological spaces are characterized by an easy ultrafilterinterpolation property, in generalization of a recent result by Pisani for spaces. From this characterization we deduce that perfect (= proper and separated) maps are exponentiable, generalizing the classical result for compact Hausdorff spaces. Furthermore, in generalization of the WhiteheadMichael characterization of locally compact Hausdorff spaces, we characterize exponentiable maps of Top between Hausdorff spaces as restrictions of perfect maps to open subspaces.
On higher rank graph C ∗ algebras
, 2002
"... Abstract. Given a rowfinite kgraph Λ with no sources we investigate the Ktheory of the higher rank graph C ∗algebra, C ∗ (Λ). When k = 2 we are able to give explicit formulae to calculate the Kgroups of C ∗ (Λ). The Kgroups of C ∗ (Λ) for k> 2 can be calculated under certain circumstances. ..."
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Cited by 10 (1 self)
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Abstract. Given a rowfinite kgraph Λ with no sources we investigate the Ktheory of the higher rank graph C ∗algebra, C ∗ (Λ). When k = 2 we are able to give explicit formulae to calculate the Kgroups of C ∗ (Λ). The Kgroups of C ∗ (Λ) for k> 2 can be calculated under certain circumstances. We state that for all k, the torsionfree rank of K0(C ∗ (Λ)) and K1(C ∗ (Λ)) are equal when C ∗ (Λ) is unital, and we determine the position of the class of the unit of C ∗ (Λ) in K0(C ∗ (Λ)). 1.
pForm Electromagnetism on Discrete Spacetimes
, 2006
"... We investigate pform electromagnetism—with the Maxwell and KalbRamond fields as lowestorder cases—on discrete spacetimes, including the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitab ..."
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We investigate pform electromagnetism—with the Maxwell and KalbRamond fields as lowestorder cases—on discrete spacetimes, including the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitable for our purpose—a chain complex equipped with an inner product on (p + 1)cochains—we study both the classical and quantum versions of the theory, with either R or U(1) as gauge group. We find results—such as a ‘pform Bohm–Aharonov effect’—that depend in interesting ways on the cohomology of spacetime. We quantize the theory via the Euclidean path integral formalism, where the natural kernels in the U(1) theory are not Gaussians but theta functions. As a special case of the general theory, we show pform electromagnetism in p + 1 dimensions has an exact solution which reduces when p = 1 to the abelian case of 2d YangMills theory as studied by Migdal and Witten. Our main result describes pform electromagnetism as a ‘chain field theory’—a theory analogous to a topological quantum field theory, but with chain complexes replacing manifolds. This makes precise a notion of time evolution in the context of discrete spacetimes of arbitrary topology.
Exponentiable morphisms: posets, spaces, locales
 and Grothendieck toposes, Theory and Applications of Categories 8
, 2000
"... ABSTRACT. Inthis paper, we consider those morphisms p: P − → B of posets for which the induced geometric morphism of presheaf toposes is exponentiable in the category of Grothendieck toposes. In particular, we show that a necessary condition is that the induced map p ↓ : P ↓ − → B ↓ is exponentiable ..."
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Cited by 8 (5 self)
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ABSTRACT. Inthis paper, we consider those morphisms p: P − → B of posets for which the induced geometric morphism of presheaf toposes is exponentiable in the category of Grothendieck toposes. In particular, we show that a necessary condition is that the induced map p ↓ : P ↓ − → B ↓ is exponentiable in the category of topological spaces, where P ↓ is the space whose points are elements of P and open sets are downward closed subsets of P. Along the way, we show that p ↓ : P ↓ − → B ↓ is exponentiable if and only if p: P − → B is exponentiable in the category of posets and satisfies an additional compactness condition. The criteria for exponentiability of morphisms of posets is related to (but weaker than) the factorizationlifting property for exponentiability of morphisms in the
Monads and Modularity
"... This paper argues that the core of modularity problems is an understanding of how individual components of a large system interact with each other, and that this interaction can be described by a layer structure. We propose a uniform treatment of layers based upon the concept of a monad. The combina ..."
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Cited by 7 (5 self)
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This paper argues that the core of modularity problems is an understanding of how individual components of a large system interact with each other, and that this interaction can be described by a layer structure. We propose a uniform treatment of layers based upon the concept of a monad. The combination of different systems can be described by the coproduct of monads.
Exponentiability in Categories of Lax Algebras
, 2003
"... For a complete cartesianclosed category V with coproducts, and for any pointed endofunctor T of the category of sets satisfying a suitable BeckChevalleytype condition, it is shown that the category of lax reflexive (T , V)algebras is a quasitopos. This result encompasses many known and new examp ..."
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Cited by 7 (3 self)
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For a complete cartesianclosed category V with coproducts, and for any pointed endofunctor T of the category of sets satisfying a suitable BeckChevalleytype condition, it is shown that the category of lax reflexive (T , V)algebras is a quasitopos. This result encompasses many known and new examples of quasitopoi. 1.
Quantum energy inequalities and local covariance II: Categorical formulation
, 2006
"... We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural ..."
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Cited by 6 (5 self)
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We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated. 1
The fiber of functors between categories of algebras
"... Abstract. We investigate the fiber of a functor F: C → D between sketchable categories of algebras over an object D ∈ D from two points of view: characterizing its classifying space as a universal Aut(D)space, and parametrizing its objects in cohomological terms. ..."
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Abstract. We investigate the fiber of a functor F: C → D between sketchable categories of algebras over an object D ∈ D from two points of view: characterizing its classifying space as a universal Aut(D)space, and parametrizing its objects in cohomological terms.