Results 11  20
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159
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' retraction pair ..."
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Cited by 21 (0 self)
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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...
Developing Theories of Types and Computability via Realizability
, 2000
"... We investigate the development of theories of types and computability via realizability. ..."
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Cited by 20 (6 self)
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We investigate the development of theories of types and computability via realizability.
Hypercohomology spectra and Thomason’s descent theorem
 IN ALGEBRAIC KTHEORY, FIELDS INSTITUTE COMMUNICATIONS
, 1997
"... The celebrated LichtenbaumQuillen conjectures predict that for a sufficiently nice scheme and given prime ℓ, the ℓadic algebraic Kgroups of X are closely related to the ℓadic étale cohomology groups of X. More precisely, one version of the conjectures asserts that there is a descent spectral se ..."
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Cited by 20 (2 self)
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The celebrated LichtenbaumQuillen conjectures predict that for a sufficiently nice scheme and given prime ℓ, the ℓadic algebraic Kgroups of X are closely related to the ℓadic étale cohomology groups of X. More precisely, one version of the conjectures asserts that there is a descent spectral sequence of AtiyahHirzebruch type H p q ét (X; Zℓ ()) ⇒ πq−p(KX 2 ℓ) but with the convergence only valid in sufficiently high degrees. Here the coefficient sheaves are Tate twists of the ℓadic integers, and are to be interpreted as zero if q is odd. Throughout this paper, étale cohomology is continuous étale cohomology [19], and the indicated abutment of the spectral sequence consists of the homotopy groups of the Bousfield ℓadic completion of the spectrum KX, not the naive ℓadic completion of the Kgroups. In a remarkable paper [42], Thomason proved the LichtenbaumQuillen conjectures for a certain localized form of Ktheory socalled “Bottperiodic” Ktheory. The first step was the development of an elaborate theory of hypercohomology spectra H ·(X; E) associated to étale presheaves of spectra E or more generally, to presheaves of spectra on a Grothendieck site. These hypercohomology spectra are by their very construction naturally Supported by a grant from the National Science Foundation 1 equipped with a suitable descent spectral sequence, and there is a natural map E(X)−→H · (X; E). In particular, the Ktheory of a scheme X maps to its associated hypercohomology spectrum H · ét(X; K). Fix a prime ℓ, which we will assume is odd in order to simplify the discussion.Let L(−) denote Bousfield localization with respect to complex Ktheory, and let ˆ L(−) denote its ℓadic completion. The main theorem of [42] can be stated as follows. Theorem 0.1 Let X be a separated noetherian regular scheme of finite Krull dimension, with sufficiently nice residue fields of characteristic different from ℓ. Then the natural map KX−→H · ét(X; K) induces a weak equivalence
Topical Categories of Domains
, 1997
"... this paper are algebraic dcpos, and many of the points discussed here will be needed later in the special case. 2 They provide a simple example to illustrate the "Display categories" in Section 3.2 ..."
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Cited by 18 (17 self)
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this paper are algebraic dcpos, and many of the points discussed here will be needed later in the special case. 2 They provide a simple example to illustrate the "Display categories" in Section 3.2
Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Cited by 17 (6 self)
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Intuitionistic Choice and Classical Logic
 Arch. Math. Logic
, 1997
"... this paper we show how to combine the unrestricted countable choice, induction on infinite wellfounded trees and restricted classical logic in a constructively given model. For readers faniliar with intuitionistic systems [14], we may succinctly describe the theory we interpret as follows. Expand t ..."
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Cited by 16 (4 self)
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this paper we show how to combine the unrestricted countable choice, induction on infinite wellfounded trees and restricted classical logic in a constructively given model. For readers faniliar with intuitionistic systems [14], we may succinctly describe the theory we interpret as follows. Expand the extensional version of HA
Geometric Theories and Databases
 APPLICATIONS OF CATEGORIES IN COMPUTER SCIENCE, VOLUME 177 OF LONDON MATHEMATICAL SOCIETY LECTURE NOTES
, 1992
"... Domain theoretic understanding of databases as elements of powerdomains is modified to allow multisets of records instead of sets. This is related to geometric theories and classifying toposes, and it is shown that algebraic base domains lead to algebraic categories of models in two cases analogous ..."
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Domain theoretic understanding of databases as elements of powerdomains is modified to allow multisets of records instead of sets. This is related to geometric theories and classifying toposes, and it is shown that algebraic base domains lead to algebraic categories of models in two cases analogous to the lower (Hoare) powerdomain and Gunter's mixed powerdomain.
Modified Realizability Toposes and Strong Normalization Proofs (Extended Abstract)
 Typed Lambda Calculi and Applications, LNCS 664
, 1993
"... ) 1 J. M. E. Hyland 2 C.H. L. Ong 3 University of Cambridge, England Abstract This paper is motivated by the discovery that an appropriate quotient SN 3 of the strongly normalising untyped 3terms (where 3 is just a formal constant) forms a partial applicative structure with the inherent appl ..."
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) 1 J. M. E. Hyland 2 C.H. L. Ong 3 University of Cambridge, England Abstract This paper is motivated by the discovery that an appropriate quotient SN 3 of the strongly normalising untyped 3terms (where 3 is just a formal constant) forms a partial applicative structure with the inherent application operation. The quotient structure satisfies all but one of the axioms of a partial combinatory algebra (pca). We call such partial applicative structures conditionally partial combinatory algebras (cpca). Remarkably, an arbitrary rightabsorptive cpca gives rise to a tripos provided the underlying intuitionistic predicate logic is given an interpretation in the style of Kreisel's modified realizability, as opposed to the standard Kleenestyle realizability. Starting from an arbitrary rightabsorptive cpca U , the tripostotopos construction due to Hyland et al. can then be carried out to build a modified realizability topos TOPm (U ) of nonstandard sets equipped with an equali...
From Coherent Structures to Universal Properties
 J. Pure Appl. Algebra
, 1999
"... Given a 2category K admitting a calculus of bimodules, and a 2monad T on it compatible with such calculus, we construct a 2category L with a 2monad S on it such that: • S has the adjointpseudoalgebra property. • The 2categories of pseudoalgebras of S and T are equivalent. Thus, coh ..."
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Given a 2category K admitting a calculus of bimodules, and a 2monad T on it compatible with such calculus, we construct a 2category L with a 2monad S on it such that: • S has the adjointpseudoalgebra property. • The 2categories of pseudoalgebras of S and T are equivalent. Thus, coherent structures (pseudoTalgebras) are transformed into universally characterised ones (adjointpseudoSalgebras). The 2category L consists of lax algebras for the pseudomonad induced by T on the bicategory of bimodules of K. We give an intrinsic characterisation of pseudoSalgebras in terms of representability. Two major consequences of the above transformation are the classifications of lax and strong morphisms, with the attendant coherence result for pseudoalgebras. We apply the theory in the context of internal categories and examine monoidal and monoidal globular categories (including their monoid classifiers) as well as pseudofunctors into Cat.