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Solving Recursive Domain Equations with Enriched Categories
, 1994
"... Both preorders and metric spaces have been used at various times as a foundation for the solution of recursive domain equations in the area of denotational semantics. In both cases the central theorem states that a `converging' sequence of `complete' domains/spaces with `continuous' ..."
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Both preorders and metric spaces have been used at various times as a foundation for the solution of recursive domain equations in the area of denotational semantics. In both cases the central theorem states that a `converging' sequence of `complete' domains/spaces with `continuous' retraction pairs between them has a limit in the category of complete domains/spaces with retraction pairs as morphisms. The preorder version was discovered first by Scott in 1969, and is referred to as Scott's inverse limit theorem. The metric version was mainly developed by de Bakker and Zucker and refined and generalized by America and Rutten. The theorem in both its versions provides the main tool for solving recursive domain equations. The proofs of the two versions of the theorem look astonishingly similar, but until now the preconditions for the preorder and the metric versions have seemed to be fundamentally different. In this thesis we establish a more general theory of domains based on the noti...
Sheaves over Right Sided Idempotent Quantales
 Journal of the IGPL
, 1998
"... We present a discussion of sheaves and presheaves over a right sided idempotent quantale in a fashion that is similar to the way that these objects are conceived over complete Heyting algebras by Fourman and Scott in [5]. Keywords : quantales, Qsets, sheaf, characteristic maps, firstorder quantifi ..."
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We present a discussion of sheaves and presheaves over a right sided idempotent quantale in a fashion that is similar to the way that these objects are conceived over complete Heyting algebras by Fourman and Scott in [5]. Keywords : quantales, Qsets, sheaf, characteristic maps, firstorder quantifiers The idea of a quantale originated with C.J.Mulvey ([6]) as an attempt to code a lattice theoretic construct that might be appropriate to obtain, for non commutative C # algebras, an analogue of the classical duality between commutative C # algebras and compact Hausdor# spaces. We cite [8] as a general reference on the circle of ideas connected with quantales. A number of authors have studied the possibility of extending the notions of sheaf and presheaf over a complete Heyting algebra (cHa) or frame to this new context ([7], [2], [1], [4]). It should be mentioned that an exposition of the content of [2] can be found in [8]. We consider [5] as a basic reference for presheaves and sheaves...
Developments in N oncommutative Differential Geometry
, 2002
"... Use policy The fulltext may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or notforprofit purposes provided that: • a full bibliographic reference is made to the original source • a l ..."
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Use policy The fulltext may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or notforprofit purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham ETheses • the fulltext is not changed in any way The fulltext must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham ETheses policy for further details.