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Arrow categories
, 2007
"... Abstract. Goguen categories were introduced as a suitable categorical description of Lfuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study the algebraic structures de ..."
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Cited by 1 (0 self)
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Abstract. Goguen categories were introduced as a suitable categorical description of Lfuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study the algebraic structures
ON THE ARROW OF TIME
, 708
"... Abstract. The interface between classical physics and quantum physics is explained from the point of view of Quantum Information Theory (Feynman Processes), based on the qubit model. The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. As a benefit, the wa ..."
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Cited by 8 (2 self)
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Abstract. The interface between classical physics and quantum physics is explained from the point of view of Quantum Information Theory (Feynman Processes), based on the qubit model. The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. As a benefit
A new notation for arrows
 In International Conference on Functional Programming (ICFP ’01
, 2001
"... The categorical notion of monad, used by Moggi to structure denotational descriptions, has proved to be a powerful tool for structuring combinator libraries. Moreover, the monadic programming style provides a convenient syntax for many kinds of computation, so that each library defines a new sublang ..."
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Cited by 65 (1 self)
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sublanguage. Recently, several workers have proposed a generalization of monads, called variously “arrows ” or Freydcategories. The extra generality promises to increase the power, expressiveness and efficiency of the embedded approach, but does not mesh as well with the native abstraction and application
Arrows and computation
 The Fun of Programming
, 2003
"... With this machinery, we can give a common structure to programs based on different notions of computation. The generality of arrows tends to force one into a pointfree style, which is useful for proving general properties. However it is not to everyone's taste, and can be awkward for programmi ..."
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Cited by 14 (0 self)
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With this machinery, we can give a common structure to programs based on different notions of computation. The generality of arrows tends to force one into a pointfree style, which is useful for proving general properties. However it is not to everyone's taste, and can be awkward
CATEGORY
"... group. Details are in [5]. 1. The center of a tensor category The center of a tensor category was defined by Drinfeld, Joyal and Street ([3]), and Magid ([4]). We review the definition. Let $\mathcal{A} $ be a tensor category over a field. The tensor product of objects $A, $ $B\in \mathcal{A} $ is d ..."
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$ as $XY $ , and the disjoint sum of $X $ and $Y $ as $X+Y$. Let $k $ be a field. Denote by $\mathcal{V} $ the category of vector spaces over $k $. A Mackey functor $M $ on $S $ consists of kvector spaces $M(X) $ for all Gsets $X $ and linear maps $f_{*}: $ $M(X)arrow M(Y) $ and $f^{*}: $ $M(Y)arrow M
Matrices As Arrows
"... There are several domain specific languages to represent matrices and related linear algebra algorithms as multiplication, transforms and Gaussian elimination. These arise as dialects with no formal foundations and lack of semantic richness as types. Interestingly a successful language [1], used in ..."
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there was the need to use matrix product as the basic matrix composition operator and matrices are viewed and transformed indexfree. This matches the categorical characterization of matrices which can be traced back to [3] whereas each matrix is denoted as an arrow between its dimensions i.e. the natural numbers
Kenneth Arrow
, 2001
"... Under the Oil Pollution Act of 1990, the Presidentacting through the Under Secretary of Commerce for Oceans and ..."
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Under the Oil Pollution Act of 1990, the Presidentacting through the Under Secretary of Commerce for Oceans and
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