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Topic: Universal constructions

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Adjoint functors

Monic morphism

Kolmogorov space

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	Adjoint functors (Site not responding. Last check: 2007-11-06)
		Similarly, the group ring construction yields a functor from groupss to rings, left adjoint to the functor that assigns to a given ring its group of units.
		All pairs of adjoint functors arise from universal constructions.
		Universal constructions are more general than adjoint functor pairs: as mentioned earlier, a universal construction is like an optimization problem; it gives rise to an adjoint pair if and only if this problem has a solution for every object of D.
	www.bidprobe.com /en/wikipedia/a/ad/adjoint_functors.html (3145 words)

	Category theory - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-06)
		Furthermore, different such constructions are often "naturally related" which leads to the concept of natural transformation, a way to "map" one functor to another.
		Universal constructions: Functors are often defined by universal properties; examples are the tensor product discussed above, the direct sum and direct product of groups or vector spaces, construction of free groups and modules, direct and inverse limits.
		Universal constructions often give rise to pairs of adjoint functors.
	encyclopedia.learnthis.info /c/ca/category_theory.html (3218 words)

	Practical Foundations of Mathematics (Site not responding. Last check: 2007-11-06)
		Universal properties galore have arisen in the earlier chapters, and it is high time we gave a unified framework for them.
		In 1948 Pierre Samuel identified universal properties as a common formulation of several constructions in topology, and the Bourbaki school used them in their comprehensive account of mathematics.
		Often the thing which is required is obtained as a composite of two universal constructions: recognising it as such makes the development more modular.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s70.html (438 words)

	Michiel Hazewinkel : Book review (Site not responding. Last check: 2007-11-06)
		This book is devoted to studing the fundamentals of the theory of Boolean constructions in universal algebras, to the problems of presenting different varieties of universal algebras with these constructions and to the use of Boolean constructions for investigating the spectra and skeletons of varieties of universal algebras.
		One of the basic ways the theory of Boolean algebras has been affecting the theory of universal algebras on the whole during the last decades, has been the introduction and wide use of the construction of Boolean powers and their various modifications in universal algebra (chapter 2).
		The aim of the chapter 3 is to apply the methods, results and constructions considered in the first two chapters to studies of universal algebra varieties.
	homepages.cwi.nl /~mich/reviews/AAA_1111.html (216 words)

	Universal Constructions for Large Objects - Anderson, Moir (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Most previous universal constructions require processes to copy the entire object state, which is impractical for large objects.
		A universal construction for n processes is an algorithm that, when instantiated with the sequential implementation...
		A (non blocking or waitfree) universal construction for n processes is an algorithm that, when instantiated...
	citeseer.ist.psu.edu /10894.html (525 words)

	Androidal Systems
		Because machine languages are viewed through the universal grammar as "high-level languages," both the source and object codes are construed simply as ordinary languages translated by the system's universal translation capabilities.
		Because both the physical system and the model are understood by the KP from the standpoint of the universal grammar, and because the model system is embodied in the hardware of the knowledge processing platform, the KP accomplishes both the design and implementation of a physical system in the same technological scenario, as illustrated below.
		In advancing the art of artificial intelligence, ASI has taken the novel approach of constructing an "android," or a machine being guided by an endless synthetic "consciousness." The android is controlled by the manipulation of language-words from Roget's thesaurus-in correspondence with its physical and mental activities.
	www.androidal.com /pages/prodapps.html (2543 words)

	6.3.1 Examplary Constructions of the Universal Graph
		The geometry of the orbit structure and the universal graph are depicted in Fig.
		We are able to construct the representation of the dimensional function independent of the particular choice of the dimensional basis.
		Geometrically (6.16) represents the plane and the universal graph is also the intersection of this plane with the surface (6.15).
	www.immt.pwr.wroc.pl /kniga/node29.html (4649 words)

	Practical Foundations of Mathematics
		A,A is universal iff it is a coproduct diagram.
		UA is universal iff it is a colimiting cocone.
		If we take the semantic option, then the universal property of the classifying category is more complicated than Definition 7.1.1: the interpretation functor [[-]] is only unique up to unique isomorphism - if it is defined at all, as some Choice is to be made.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s71.html (1926 words)

	Cryptology ePrint Archive (Site not responding. Last check: 2007-11-06)
		Golle et al introduced universal re-encryption, defining it as re- encryption by a player who does not know the key used for the original encryption, but which still allows an intended player to recover the plaintext.
		Universal re-encryption is potentially useful as part of many information-hiding techniques, as it allows any player to make ciphertext unidentifiable without knowing the key used.
		Golle et al’s techniques for universal re-encryption are reviewed, and improved constructions for both simple and hybrid universal re-encryption systems are presented, including a hybrid construction that permits indefinite re-encryptions with better efficiency and an almost-optimally small increase in file size.
	eprint.iacr.org /2003/255 (122 words)

	[No title]
		The universal Leibniz delta operator corresponds to the universal formal group law and to the universal complex-oriented cohomology theory of unitary cobordism.
		E): The classical Hattori-Stong theorem asserts that when E is the universal* delta operator, the quotient of this inclusion is a torsion free abelian group (or equivalently, that the subgroup L(E)* is pure).
		Universal examples We now explain how to construct a universal (e; f)-operator for fixed delta operators E and F, and then describe a particular case which is also universal for all double delta operators.
	hopf.math.purdue.edu /Clarke-Hunton-Ray/euc2.txt (8903 words)

	ASCO Valve (Site not responding. Last check: 2007-11-06)
		Air operated valves available in universal construction with brass bodies and NBR seats.
		Pilot operated solenoid valves available in a universal construction available with brass and stainless steel bodies.
		AC operated solenoid pilot operated diaphragm valves available in normally closed and normally open constructions with Brass bodies for a wide variety of high flow applications.
	www.ascovalve.com /products_detail.asp?detail=solenoid_3way_data (994 words)

	DISI
		In category theory, the important constructions are given by means of coherence structures which control the data algebraically.
		In information technology, constructive type theory has been developed in the introduction of the so-called functional programming languages, and in the analysis of the properties of programs such as correctness of the code with respect to a given specification, termination, and reachability.
		We are also try to obtain a direct connection between constructive type theory and universal constructions, since all these have an extemely explicit, finitary presentation.
	www.disi.unige.it /index.php?research/pl-lct (306 words)

	Michiel Hazewinkel : Book review (Site not responding. Last check: 2007-11-06)
		This monograph is devoted to studying the fundamentals of the theory of Boolean construction in universal algebras.
		The problem of presenting different varieties of universal algebras are presented in Chapter 2: boolean power, Heyting algebras, Lukasiewicz algebras of the order n, cylindric algebras of dimension n, relation algebras and rings.
		The use of Boolean construction for investigating the spectra, skeleton and categories of varieties of universal algebra is presented in Chapter 3.
	homepages.cwi.nl /~mich/reviews/AAA_1245.html (156 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Subject: universality of gfs From: Farrell Ackerman Date: Sun, 14 Jun 1998 13:44:10 -0700 for what it's worth, here's my private collection of misunderstandings concerning rachel's inquiry: it's easy to agree with both paul and joan concerning the distinction between a formalism and the vision of grammar implemented within a formalism.
		given this, it's possible to imagine a kind of lfg without gfs (if it proves that this is empirically necessary) and it's possible to imagine a kind of cg containing a theory of universals (if this proves desirable).
		I know that this is supposed to follow from the claim that both phrases (including sentences) and morphology are "constructions", but i'm not really sure that I know what this means in practice.
	www-lfg.stanford.edu /lfg/clwww.essex.ac.uk/LFG/Mail-list/98/980615124137 (467 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		------------------------------------------------------------------------------ Universal Construction for the FKS Scheme (Chee Yap) The problem of optimal static hashing was first solved in general by Fredman, Komlos and Szemeredi (FKS).
		We introduce a new analysis of the FKS construction, making a direct connection with the universality concepts of Carter and Wegman.
		Our result represents a new application of universal hashing: given any strongly universal hash set H, one can construct a FKS scheme based on H. We resolve a question first raised by the FKS paper: whether it is possible to use hash functions that avoid arithmetic on "large" numbers and the use of primes.
	www.cgc.ethz.ch /external/colloquia/1999-S/friday_talks.txt (257 words)

	Category theory - FreeEncyclopedia (Site not responding. Last check: 2007-11-06)
		Although originally developed in the context of algebraic geometry, algebraic topology and universal algebra, it is now also used in various other branches of mathematics.
		Very commonly, certain "natural constructions", such as the fundamental group, can be expressed as functors.
		One may check that the map from the category of Hausdorff topological spaces with a distinguished point to the category of groups is functorial: a topological (homo/iso)morphism will naturally correspond to a group (homo/iso)morphism.
	openproxy.ath.cx /ca/Category_theory.html (2075 words)

	A Lower Bound on the Local Time Complexity of Universal Constructions - Jayanti (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: Non-blocking and wait-free universal constructions have been a subject of active research in recent years.
		A universal construction is attractive because, no matter what types of shared objects are needed by applications, they can be implemented simply by instantiating the universal construction with appropriate types.
		This flexibility, however, comes at a cost: for each universal construction U, we prove that there is a type T such that, if O is an n-process type T object implemented using...
	citeseer.ist.psu.edu /368099.html (631 words)

	Algebraic Structures on Knotted Objects and Universal Finite Type Invariants
		The idea is to find presentations of knot theory, or of some mild generalizations of knot theory, in terms of finitely many generators and relations, and then to construct a universal finite type invariant by setting its values on the generators so as the relations are satisfied.
		J] and leads to a crossing-centric constructions of a universal finite type invariant (as opposed to the now-standard associativity-centric construction).
		This is another semi-successful algebraic approach to the construction of a universal finite type invariants via generators and relations.
	www.math.toronto.edu /~drorbn/papers/AlgebraicStructures/LongAlgebraicStructures.html (2740 words)

	Functor (Site not responding. Last check: 2007-11-06)
		There are many constructions in mathematics which would be functors but for the fact that they "turn morphisms around" and "reverse composition".
		Likewise, the map which sends every differentiable manifold to its cotangent bundle and every smooth map to its pullback is a contravariant functor.
		Doing these constructions pointwise gives covariant and contravariant functors from the category of pointed differentiable manifolds to the category of real vector spaces.
	www.yotor.com /wiki/en/fu/Functor.htm (1530 words)

	Table of contents for Library of Congress control number 2001036596
		Syntactic and semantic structure: the anatomy of a construction 1.3.3.
		The organization of constructions in a construction grammar 1.4.
		Semantic Universals, Relativity, and Radical Construction Grammar 4.
	www.loc.gov /catdir/toc/fy022/2001036596.html (547 words)

	George M. Bergman -- publications and preprints
		An Invitation to General Algebra and Universal Constructions, pub.
		Open problems discussed at a conference in honor of Walter Taylor at the University of Colorado, 15-18 August, 2004, 7 pp., last revised 26 March, 2005. (I'm just the record-keeper for this collection, but I decided my preprint list was the best place to post it.)
		Universal derivations and universal ring constructions (with Warren Dicks), Pacific J. Math.
	math.berkeley.edu /~gbergman/papers (1346 words)

	Universal Constructions in Umbral Calculus - Ray (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Universal Constructions in Umbral Calculus - Ray (ResearchIndex)
		Abstract: Introduction Modern umbral calculus is steadily approaching maturity, as applications develop in several areas of mathematics.
		Ray, Universal constructions in umbral calculus, to appear in the Proceedings of the Rotafest, April 1996.
	citeseer.ist.psu.edu /ray96universal.html (525 words)

	Classifier constructions in sign languages (Site not responding. Last check: 2007-11-06)
		The focus of this presentation is the grammatical structure and cross-linguistic variation of classifier constructions in sign languages (a.k.a.
		Early research suggested that these forms can be analyzed as combinations of discrete morphemes, specifically, as predicates consisting of one or more movement roots along with several other morphemes encoding the shape or semantic class of object involved (indicated by a classifier handshape), the location, and the orientation of the object.
		Since classifier constructions are universal to all sign languages encountered thus far, it is important to build a consensus on what counts as a classifier and to begin to document the nature and extent of cross-linguistic variation.
	psy.ucsd.edu /~kemmorey/lgproc/TISLR00cl.abs.html (275 words)

	Universal Constructions for Large Objects (Site not responding. Last check: 2007-11-06)
		We present lock-free and wait-free universal constructions for implementing large shared objects.
		In contrast, our constructions are designed to largely shield programmers from this fragmentation.
		Fragmentation is achieved in our constructions through the use of load-linked, store-conditional, and validate operations on a “large” multiword shared variable.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/td/&toc=comp/trans/td/1999/12/lztoc.xml&DOI=10.1109/71.819952 (326 words)

	Categories for Software Engineering
		Part I covers some of the basics of category theory, including the “bare essentials” that are addressed in any book, from graphs to universal constructions and functors.
		It is hoped that mathematically mature readers may appreciate a different way of exposing and illustrating these familiar concepts and constructions.
		Again, examples are drawn from areas that have normally been confined to papers such as institutions and models of concurrency.
	www.fiadeiro.org /jose/CATBook (379 words)

	Atlas: Fully embedding (sober) topological spaces in a category of coalgebras with a sequence of three universal ... (Site not responding. Last check: 2007-11-06)
		Clearly, in such a construction some properties of Sets are lost, notably the cartesian product looses his cartesianess, and the (regular epi)-(mono) factorization of a map is not available anymore as a stable, proper factorization system.
		We show that freely adding the last property to the result of the first ``free'' construction, and cofreely adding the first property to the result, we get a category of coalgebras and the claimed full embedding, which is in fact a coreflection.
		Eventhough the category of coalgebras so constructed has a plain direct description, the description by universal properties, and in particular by the second one, is quite useful to investigate the full embedding and his properties.
	atlas-conferences.com /cgi-bin/abstract/cajf-43 (220 words)

	Category Theory for Computer Science (Site not responding. Last check: 2007-11-06)
		Autumn 2002 - Department of Computer Science - University of Aarhus
		universal constructions in a poset viewed as a category (meet, join, top, bottom)
		All the material can be obtained from the project consultant.
	www.daimi.au.dk /~nygaard/CTfCS (620 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations (Site not responding. Last check: 2007-11-06)
		We address the problem of universality in simulation of evolution of quantum system and in theory of quantum computations related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific unitary transformations (quantum gates) from given set.
		In an earlier paper application of Clifford algebras to constructions of universal sets of binary quantum gates U{sub k} is a subset of U(2{sup n}) was shown.
		A set of universal nonbinary two-gates is presented here as one example.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20420132 (244 words)

	I&C Technical Reports (Site not responding. Last check: 2007-11-06)
		A universal construction is an algorithm that transforms any object with a sequential specification into a wait-free and linearizable implementation of that object.
		This paper presents a novel universal construction algorithm for a message-passing system with process crash failures.
		Our algorithm is generic in two senses: (1) it is initially devised for a crash-stop model and can be easily ported to various crash-recovery models, and (2) it is initially optimized for the steady-state period but can easily be extended to trade-off between steady-state performance and fail-over time.
	ic2.epfl.ch /publications/abstract.php?ID=200228 (165 words)

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