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Sheaf Cohomology
, 2003
"... In this lecture, we define the cohomology groups of a topological space X with coefficients in a sheaf of abelian groups F on X in terms of the derived functors of the global section functor Γ(X, ·). Then we introduce Čech cohomology with respect to an open covering of X, which permits to make expl ..."
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In this lecture, we define the cohomology groups of a topological space X with coefficients in a sheaf of abelian groups F on X in terms of the derived functors of the global section functor Γ(X, ·). Then we introduce Čech cohomology with respect to an open covering of X, which permits to make
Sheaf Toposes for Realizability
, 2001
"... We compare realizability models over partial combinatory algebras by embedding them into sheaf toposes. We then use the machinery of Grothendieck toposes and geometric morphisms to study the relationship between realizability models over di#erent partial combinatory algebras. This research is part o ..."
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We compare realizability models over partial combinatory algebras by embedding them into sheaf toposes. We then use the machinery of Grothendieck toposes and geometric morphisms to study the relationship between realizability models over di#erent partial combinatory algebras. This research is part
Sheaf Representation for Topoi
, 1997
"... It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of socalled hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of wellpointed topoi. Completeness ..."
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It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of socalled hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of wellpointed topoi. Completeness
Sheaf and Trace Models of Concurrency
, 1993
"... We relate sheaf and trace models of concurrency for an interacting community of objects with a discrete linear infinitary model of time. The sheaf model can be more easily generalized for other assumptions about time, and has broader connections to other models of concurrency. The traces model is mo ..."
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We relate sheaf and trace models of concurrency for an interacting community of objects with a discrete linear infinitary model of time. The sheaf model can be more easily generalized for other assumptions about time, and has broader connections to other models of concurrency. The traces model
Sheaf Theoretic Formulation of Entanglement
"... A formulation in terms of sheaf theoretic (or categorical) notions for quantum entanglement is given with direct experimental consequences. The notions from sheaf theory and category theory give structural theory, i.e., qualitative theory, as a candidate for quantum gravity. Its advantage is the fol ..."
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A formulation in terms of sheaf theoretic (or categorical) notions for quantum entanglement is given with direct experimental consequences. The notions from sheaf theory and category theory give structural theory, i.e., qualitative theory, as a candidate for quantum gravity. Its advantage
SHEAFTHEORETIC FORMAL SEMANTICS
"... Abstract. We outline a sheaftheoretical framework for a discourse interpretation theory developed in our previous works on formal semantics. This theory applies rigorous mathematical methods in studying the process of interpretation of a natural language text written with good grace and intended f ..."
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Abstract. We outline a sheaftheoretical framework for a discourse interpretation theory developed in our previous works on formal semantics. This theory applies rigorous mathematical methods in studying the process of interpretation of a natural language text written with good grace and intended
SHEAF REPRESENTATION OF NORMED SPACES
"... Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding to the cohe ..."
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Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding
Generalised Sheaf Cohomology Theories
, 2003
"... This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled "Homotopy Theory of Geometric Categories" on September 23 and 24, 2002. This workshop was part of a program entitled New Contex ..."
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This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled "Homotopy Theory of Geometric Categories" on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002
Results 1  10
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13,195