Category Theory In Context

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Category Theory In Context

Author : Emily Riehl
ISBN : 9780486820804
Genre : Mathematics
File Size : 70.30 MB
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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Category: Mathematics

Category Theory For Computing Science

Author : Michael Barr
ISBN : UOM:39015034447873
Genre : Mathematics
File Size : 83.59 MB
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A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.
Category: Mathematics

Intelligence And Spirit

Author : Reza Negarestani
ISBN : 9780997567403
Genre : Philosophy
File Size : 28.96 MB
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A critique of both classical humanism and dominant trends in posthumanism that formulates the ultimate form of intelligence as a theoretical and practical thought unfettered by the temporal order of things. In Intelligence and Spirit Reza Negarestani formulates the ultimate form of intelligence as a theoretical and practical thought unfettered by the temporal order of things, a real movement capable of overcoming any state of affairs that, from the perspective of the present, may appear to be the complete totality of history. Intelligence pierces through what seems to be the totality or the inevitable outcome of its history, be it the manifest portrait of the human or technocapitalism as the alleged pilot of history. Building on Hegel's account of Geist as a multiagent conception of mind and on Kant's transcendental psychology as a functional analysis of the conditions of possibility of mind, Negarestani provides a critique of both classical humanism and dominant trends in posthumanism. The assumptions of the former are exposed by way of a critique of the transcendental structure of experience as a tissue of subjective or psychological dogmas; the claims of the latter regarding the ubiquity of mind or the inevitable advent of an unconstrained superintelligence are challenged as no more than ideological fixations which do not stand the test of systematic scrutiny. This remarkable fusion of continental philosophy in the form of a renewal of the speculative ambitions of German Idealism and analytic philosophy in the form of extended thought-experiments and a philosophy of artificial languages opens up new perspectives on the meaning of human intelligence and explores the real potential of posthuman intelligence and what it means for us to live in its prehistory.
Category: Philosophy

Category Theory And Computer Science

Author : P. L. Curien
ISBN : 038754495X
Genre : Computers
File Size : 48.64 MB
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"The papers in this volume were presented at the fourth biennial Summer Conference on Category Theory and Computer Science, held in Paris, September3-6, 1991. Category theory continues to be an important tool in foundationalstudies in computer science. It has been widely applied by logicians to get concise interpretations of many logical concepts. Links between logic and computer science have been developed now for over twenty years, notably via the Curry-Howard isomorphism which identifies programs with proofs and types with propositions. The triangle category theory - logic - programming presents a rich world of interconnections. Topics covered in this volume include the following. Type theory: stratification of types and propositions can be discussed in a categorical setting. Domain theory: synthetic domain theory develops domain theory internally in the constructive universe of the effective topos. Linear logic: the reconstruction of logic based on propositions as resources leads to alternatives to traditional syntaxes. The proceedings of the previous three category theory conferences appear as Lecture Notes in Computer Science Volumes 240, 283 and 389"--PUBLISHER'S WEBSITE.
Category: Computers

Mathematical Reviews

Author :
ISBN : UOM:39015062317188
Genre : Mathematics
File Size : 37.79 MB
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Category: Mathematics

Categories For Quantum Theory

Author : Chris Heunen
ISBN : 9780198739623
Genre : Mathematics
File Size : 28.22 MB
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Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
Category: Mathematics

Engineering Of Computer Based Systems

Author : IEEE Computer Society. Technical Committee on the Engineering of Computer Based Systems
ISBN : 0769515495
Genre : Computers
File Size : 90.74 MB
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Papers from an April 2002 conference, 25 in all, report on academic achievements and industrial applications in the engineering of computer-based systems. Contributors represent some 12 countries and a variety of application domains. Papers deal with themes of requirements engineering, processes and tools, system properties and methods, modeling and analysis, system architecture, model-based system development, component-based design and reuse, embedded systems, and mobile agents. Specific topics include an intelligent agent security intrusion system, managing complex temporal requirements in real-time control systems, using category theory to model software component dependencies, and advanced Petri nets for modeling mobile agent enabled interorganizational workflows. There is no subject index. Annotation copyrighted by Book News Inc., Portland, OR.
Category: Computers

Sigsoft 95

Author : Gail E. Kaiser
ISBN : UCSC:32106011396683
Genre : Computer science
File Size : 76.7 MB
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Category: Computer science

Untying The Gordian Knot

Author : Timothy E. Eastman
ISBN : 9781793639172
Genre : Philosophy
File Size : 53.68 MB
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In Untying the Gordian Knot: Process, Reality, and Context, Timothy E. Eastman proposes a new creative synthesis, the Logoi framework—which is radically inclusive and incorporates both actuality and potentiality—to show how the fundamental notions of process, logic, and relations, woven with triads of input-output-context and quantum logical distinctions, can resolve a baker’s dozen of age-old philosophic problems. Further, Eastman leverages a century of advances in quantum physics and the Relational Realism interpretation pioneered by Michael Epperson and Elias Zafiris and augmented by the independent research of Ruth Kastner and Hans Primas to resolve long-standing issues in understanding quantum physics. Adding to this, Eastman makes use of advances in information and complex systems, semiotics, and process philosophy to show how multiple levels of context, combined with relations—including potential relations—both local and local-global, can provide a grounding for causation, emergence, and physical law. Finally, the Logoi framework goes beyond standard ways of knowing—that of context independence (science) and context focus (arts, humanities)—to demonstrate the inevitable role of ultimate context (meaning, spiritual dimension) as part of a transformative ecological vision, which is urgently needed in these times of human and environmental crises.
Category: Philosophy