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26,647
Institution Morphisms
, 2001
"... Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces ..."
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Cited by 62 (16 self)
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terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper
MORPHISMS AND INVERSE PROBLEMS
"... Abstract. In order to investigate polynomial vector fields admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the affine plane. In particular, such morphisms may be used to remove degeneracies of the underlying curve. Our main result states that the ..."
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Abstract. In order to investigate polynomial vector fields admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the affine plane. In particular, such morphisms may be used to remove degeneracies of the underlying curve. Our main result states
A DEGENERATION OF STABLE MORPHISMS AND RELATIVE STABLE MORPHISMS
"... Let W → C be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of W. We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli ..."
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Cited by 6 (2 self)
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Let W → C be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of W. We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli
GEOMETRIC MORPHISMS OF REALIZABILITY TOPOSES
"... Abstract. We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the ‘constant object ’ functors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which was s ..."
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Cited by 5 (1 self)
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Abstract. We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the ‘constant object ’ functors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which
Linear Programming Duality and Morphisms
, 1998
"... In this paper we investigate the class NP ∩ coNP (or the class of problems permitting a good characterisation) from the point of view of morphisms of oriented matroids. We prove several morphismduality theorems for oriented matroids. These generalize LPduality (in form of Farkas' Lemma) and ..."
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Cited by 2 (0 self)
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In this paper we investigate the class NP ∩ coNP (or the class of problems permitting a good characterisation) from the point of view of morphisms of oriented matroids. We prove several morphismduality theorems for oriented matroids. These generalize LPduality (in form of Farkas' Lemma
Systematic design of program analysis frameworks
 In 6th POPL
, 1979
"... Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant ..."
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Cited by 771 (52 self)
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Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves on such a manifold and Taylor coefficients of periods of Hodge structures considered as functions on the moduli space of complex structures on a mirror manifold. Recently it has been realized that one can make predictions for numbers of curves of positive genera and also on CalabiYau manifolds of arbitrary dimensions. We will not describe here the complicated history of the subject and will not mention many beautiful contsructions, examples and conjectures motivated
HIVES AND THE FIBRES OF THE CONVOLUTION MORPHISM
, 705
"... Abstract. By the geometric Satake correspondence, the number of components of certain fibres of the affine Grassmannian convolution morphism equals the tensor product multiplicity for representations of the Langlands dual group. On the other hand, in the case of GLn, combinatorial objects called hiv ..."
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Cited by 2 (0 self)
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Abstract. By the geometric Satake correspondence, the number of components of certain fibres of the affine Grassmannian convolution morphism equals the tensor product multiplicity for representations of the Langlands dual group. On the other hand, in the case of GLn, combinatorial objects called
Computational LambdaCalculus and Monads
, 1988
"... The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the ..."
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Cited by 505 (7 self)
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The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model. 1 Introduction This paper is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed terms, possibly containing extra constants, corresponding to some features of the programming language under consideration. There are three approaches to proving equivalence of programs: ffl T...
Results 1  10
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26,647