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Bireflectivity
, 1999
"... Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireflectivity. Bireflective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterise them in terms of splitidempoten ..."
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Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireflectivity. Bireflective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterise them in terms of split
Optical Class: Biaxial. Bireflectance: Weak. α = 1.536(1) γ = 1.563(1) Cell Data: Space Group: P21/n [possible]. a = 6.818(2) b = 13.794(2) c = 6.756(2)
"... in massive aggregates several meters thick. Twinning observed in some crystals with extinction under polarized light at 8°. ..."
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in massive aggregates several meters thick. Twinning observed in some crystals with extinction under polarized light at 8°.
Interaction Categories and the Foundations of Typed Concurrent Programming
 In Deductive Program Design: Proceedings of the 1994 Marktoberdorf Summer School, NATO ASI Series F
, 1995
"... We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent compu ..."
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Cited by 137 (21 self)
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We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent computation and indicate how a general axiomatisation can be developed. The upshot of our approach is that traditional process calculus is reconstituted in functorial form, and integrated with type theory and functional programming.
Abstract and Concrete Categories. The Joy of Cats
, 2004
"... Contemporary mathematics consists of many different branches and is intimately related to various other fields. Each of these branches and fields is growing rapidly and is itself diversifying. Fortunately, however, there is a considerable amount of common ground — similar ideas, concepts, and constr ..."
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Cited by 107 (0 self)
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Contemporary mathematics consists of many different branches and is intimately related to various other fields. Each of these branches and fields is growing rapidly and is itself diversifying. Fortunately, however, there is a considerable amount of common ground — similar ideas, concepts, and constructions. These provide a basis for a general theory of structures.
The purpose of this book is to present the fundamental concepts and results of such a theory, expressed in the language of category theory — hence, as a particular branch of mathematics itself. It is designed to be used both as a textbook for beginners and as a reference source. Furthermore, it is aimed toward those interested in a general theory of structures, whether they be students or researchers, and also toward those interested in using such a general theory to help with organization and clarification within a special field. The only formal prerequisite for the reader is an elementary knowledge of set theory.
NON ARCHIMEDEAN METRIC INDUCED FUZZY UNIFORM SPACES
, 1988
"... ABSTRACT. It is shown that the category of nonArchimedean metric spaces with lLipschitz maps can be embedded as a coreflectlve nonbireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and unif’orm properties are derived. ..."
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ABSTRACT. It is shown that the category of nonArchimedean metric spaces with lLipschitz maps can be embedded as a coreflectlve nonbireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and unif’orm properties are derived.
SEPARATING INVARIANTS AND FINITE REFLECTION GROUPS
, 2008
"... Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a more geometric notion of separating algebra. This allows us to prove that when there is a pol ..."
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Cited by 9 (5 self)
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polynomial separating algebra, the group is generated by reflections, and when there is a complete intersection separating algebra, the group is generated by bireflections.
LGUILDS AND BINARY LMEROTOPIES
"... Abstract. The present paper is primarily concerned with the study of Lguilds in an Lmerotopic space. It is shown that every Lcluster is an Lguild; however the converse is not true. For contigual and regular Lmerotopies, where on one side we gave an example of a space, which is neither contigual ..."
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contigual nor binary, on the other side we constructed Lmerotopic spaces that are contigual and binary. It is shown that the category LBIN of binary Lmerotopic spaces and Lmerotopic maps is bireflective in LMER,
Janggunite, a new manganese hydroxide mineral from the Janggun mine, Bonghwa, Korea
"... SUMMARY. Janggunite occurs as radiating groups of flakes, flowerlike aggregates, colloform bands, dendritic or arborescenl masses in the cementation zone of the supergene manganese oxide deposits. The flakes average o'o5 mm. Colour black, lustre dull, streak brownish black to dark brown. Cleav ..."
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. Cleavage one direction perfect. H = 2 3, very fragile. D~s = 3"59, D~c = 3"58. Under reflected light anisotropic and bireflectant. No internal reflections. Etching reactions:
© Hindawi Publishing Corp. COMPLETION OF A CAUCHY SPACE WITHOUT THE T2RESTRICTION ON THE SPACE
, 1999
"... Abstract. A completion of a Cauchy space is obtained without the T2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called smaps form a subcategory CHY ′ of CHY. A completion functor is defined for th ..."
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for this subcategory. The completion subcategory of CHY ′ turns out to be a bireflective subcategory of CHY′. This theory is applied to obtain a characterization of Cauchy spaces which allow regular completion.
On the CohenMacaulay Property of Modular Invariant Rings
, 1997
"... If V is a faithful module for a finite group G over a field of characteristic p ? 0, then the ring of invariants need not be CohenMacaulay if p divides the order of G. In this article the cohomology of G is used to study the question of CohenMacaulayness of the invariant ring. Let R = S(V ) be ..."
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Cited by 19 (10 self)
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invariants of sufficiently many copies of V is not CohenMacaulay. A further result is that if G is a pgroup and R G is CohenMacaulay, then G is a bireflection group, i.e., it is generated by elements oe with rank(oe \Gamma 1) 2. Introduction Let G GL(V ) be a finite group acting on a vector space V
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