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The X Window System
 Department of Computer Engineering at the University of Istanbul. His
, 1990
"... Mining interesting association rules from customer databases and transaction databases ..."
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Cited by 12 (0 self)
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Mining interesting association rules from customer databases and transaction databases
Involutive categories and monoids, with a GNScorrespondence
 In Quantum Physics and Logic (QPL
, 2010
"... This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of EilenbergMoore algebras of involutive monads are involutive, with conjugation for modules and vecto ..."
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Cited by 4 (2 self)
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This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of EilenbergMoore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the socalled GelfandNaimarkSegal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric monoidal categories. 1
Predicate Logic for Functors and Monads
, 2010
"... Abstract. This paper starts from the elementary observation that what is usually called a predicate lifting in coalgebraic modal logic is in fact an endomap of indexed categories. This leads to a systematic review of basic results in predicate logic for functors and monads, involving induction and c ..."
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Abstract. This paper starts from the elementary observation that what is usually called a predicate lifting in coalgebraic modal logic is in fact an endomap of indexed categories. This leads to a systematic review of basic results in predicate logic for functors and monads, involving induction and coinduction principles for functors and compositional modal operators for monads. 1
Traces for Coalgebraic Components
 MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of sta ..."
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This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component diagrams. The microcosm principle then yields a canonical “inner” traced monoidal structure on the category of resumptions (elements of final coalgebras / components). This generalises an observation by Abramsky, Haghverdi and Scott.
Bohrification
, 2010
"... The aim of this chapter is to construct new foundations for quantum logic and quantum spaces. This is accomplished by merging algebraic quantum theory and topos theory (encompassing the theory of locales or frames, of which toposes in a sense form the ultimate generalization). In a nutshell, the rel ..."
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The aim of this chapter is to construct new foundations for quantum logic and quantum spaces. This is accomplished by merging algebraic quantum theory and topos theory (encompassing the theory of locales or frames, of which toposes in a sense form the ultimate generalization). In a nutshell, the relation between these fields is as follows. First, our mathematical interpretation of Bohr’s ‘doctrine of classical concepts ’ is that the empirical content of a quantum theory described by a noncommutative (unital) C*algebra A is contained in the family of its commutative (unital) C*algebras, partially ordered by inclusion. Seen as a category, the ensuing poset C(A) canonically defines the topos [C(A), Set] of covariant functors from C(A) to the category Set of sets and functions. This topos contains the ‘Bohrification ’ A of A, defined as the tautological functor C ↦ → C, as an internal commutative C*algebra. Second, according to the toposvalid Gelfand duality theorem of Banaschewski and Mulvey, A has a Gelfand spectrum Σ(A), which is a locale internal to the topos
Components Traces
, 2010
"... Abstract. This paper contributes to the theory of coalgebraic, statebased modelling of components via two additions: a feedback operator in the form of a monoidal trace, and a threedimensional string calculus for representing and manipulating composite component diagrams. The feedback operator on c ..."
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Abstract. This paper contributes to the theory of coalgebraic, statebased modelling of components via two additions: a feedback operator in the form of a monoidal trace, and a threedimensional string calculus for representing and manipulating composite component diagrams. The feedback operator on components is shown to satisfy the trace axioms by Joyal, Street and Verity. As a corollary, we appeal to the microcosm principle and derive a canonical traced monoidal structure on the category of resumptions. This generalises an observation by Abramsky, Haghverdi and Scott. 1
CMCS 2010 Categorifying Computations into Components via Arrows as Profunctors
"... The notion of arrow by Hughes is an axiomatization of the algebraic structure possessed by structured computations in general. We claim that an arrow also serves as a basic component calculus for composing statebased systems as components—in fact, it is a categorified version of arrow that does so. ..."
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The notion of arrow by Hughes is an axiomatization of the algebraic structure possessed by structured computations in general. We claim that an arrow also serves as a basic component calculus for composing statebased systems as components—in fact, it is a categorified version of arrow that does so. In this paper, following the second author’s previous work with Heunen, Jacobs and Sokolova, we prove that a certain coalgebraic modeling of components—which generalizes Barbosa’s—indeed carries such arrow structure. Our coalgebraic modeling of components is parametrized by an arrow A that specifies computational structure exhibited by components; it turns out that it is this arrow structure of A that is lifted and realizes the (categorified) arrow structure on components. The lifting is described using the first author’s recent characterization of an arrow as an internal strong monad in Prof, the bicategory of small categories and profunctors.