Category Theory for the Sciences

Author: David I. Spivak

Publisher: MIT Press

ISBN: 0262028131

Category: Computers

Page: 486

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An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.
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Basic Category Theory for Computer Scientists

Author: Benjamin C. Pierce,Benjamin C. (Professor Pierce, University of Pennsylvania),Benjamin C.. Pierce

Publisher: MIT Press

ISBN: 9780262660716

Category: Computers

Page: 100

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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial * Applications * Further Reading
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Category Theory

Author: Steve Awodey

Publisher: Oxford University Press

ISBN: 0191513822

Category: Mathematics

Page: 256

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This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads.
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Categories and Computer Science

Author: R. F. C. Walters

Publisher: Cambridge University Press

ISBN: 9780521422260

Category: Computers

Page: 166

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Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
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The Big Book of Concepts

Author: Gregory Murphy

Publisher: MIT Press

ISBN: 9780262250061

Category: Psychology

Page: 568

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Concepts embody our knowledge of the kinds of things there are in the world. Tying our past experiences to our present interactions with the environment, they enable us to recognize and understand new objects and events. Concepts are also relevant to understanding domains such as social situations, personality types, and even artistic styles. Yet like other phenomenologically simple cognitive processes such as walking or understanding speech, concept formation and use are maddeningly complex. Research since the 1970s and the decline of the "classical view" of concepts have greatly illuminated the psychology of concepts. But persistent theoretical disputes have sometimes obscured this progress. The Big Book of Concepts goes beyond those disputes to reveal the advances that have been made, focusing on the major empirical discoveries. By reviewing and evaluating research on diverse topics such as category learning, word meaning, conceptual development in infants and children, and the basic level of categorization, the book develops a much broader range of criteria than is usual for evaluating theories of concepts.
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Linguistic Categories: Auxiliaries and Related Puzzles

Volume One: Categories

Author: F. Heny,B. Richards

Publisher: Springer Science & Business Media

ISBN: 9400969899

Category: Language Arts & Disciplines

Page: 294

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VIrtually all the papers in these volumes originated in presentations at the Fourth Groningen Round Table, held in July 1980. That conference, organ ized by the Institute for General linguistics of Groningen University was the fourth in an irregular series of meetings devoted to issues of topical interest to linguists. Its predecessor, the Third Round Table, was held in June 1976, and dealt with the semantics of natural language. A selection of the papers was published as Syntax and Semantics 10, Selections from the Third Groningen Round Table, ed. by F. Heny and H. Schnelle, Academic Press, 1979. This fourth meeting was more narrowly focussed. The original intention was to examine the hypothesis of Akrnajian, Steele and Wasow in their paper 'The Category AUX in Universal Grammar', Linguistic Inquiry 10, 1-64. Ultimately the topic was broadened considerably to encompass not only the syntax, semantics and morphology of auxiliaries and related elements, but to tackle the problem (implicit in the original work of Akmajian, Steele and Wasow) of justifying the selection of categories for the analysis of natural language. In the summer of 1979, a workshop and short, informal conference were held at the University of Salzburg, in preparation for the Round Table. These were organized in conjunction with the Summer Institute of the linguistic Society of America. The cooperation of the LSA and of the University of Salzburg, and in particular of the Director of that Institute, Professor Gaberell Drachman, is hereby gratefully acknowledged.
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Innovative Assessment for the 21st Century

Supporting Educational Needs

Author: Valerie J. Shute,Betsy Jane Becker

Publisher: Springer Science & Business Media

ISBN: 9781441965301

Category: Education

Page: 257

View: 8542

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In today’s rapidly changing and information-rich world, students are not acquiring adequate knowledge and skills to prepare them for careers in mathematics, science, and technology with the traditional approach to assessment and instruction. New competencies (e.g., information communication and technology skills) are needed to deal successfully with the deluge of data. In order to accomplish this, new "educationally valuable" skills must be acknowledged and assessed. Toward this end, the skills we value and support for a society producing knowledge workers, not simply service workers, must be identified, together with methods for their measurement. Innovative Assessment for the 21st Century explores the faces of future assessment—and ask hard questions, such as: What would an assessment that captures all of the above attributes look like? Should it be standardized? What is the role of the professional teacher?
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Sorting Things Out

Classification and Its Consequences

Author: Geoffrey C. Bowker,Susan Leigh Star

Publisher: MIT Press

ISBN: 9780262261609

Category: Science

Page: 389

View: 1144

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A revealing and surprising look at how classification systems can shape both worldviews and social interactions. What do a seventeenth-century mortality table (whose causes of death include "fainted in a bath," "frighted," and "itch"); the identification of South Africans during apartheid as European, Asian, colored, or black; and the separation of machine- from hand-washables have in common? All are examples of classification—the scaffolding of information infrastructures. In Sorting Things Out, Geoffrey C. Bowker and Susan Leigh Star explore the role of categories and standards in shaping the modern world. In a clear and lively style, they investigate a variety of classification systems, including the International Classification of Diseases, the Nursing Interventions Classification, race classification under apartheid in South Africa, and the classification of viruses and of tuberculosis. The authors emphasize the role of invisibility in the process by which classification orders human interaction. They examine how categories are made and kept invisible, and how people can change this invisibility when necessary. They also explore systems of classification as part of the built information environment. Much as an urban historian would review highway permits and zoning decisions to tell a city's story, the authors review archives of classification design to understand how decisions have been made. Sorting Things Out has a moral agenda, for each standard and category valorizes some point of view and silences another. Standards and classifications produce advantage or suffering. Jobs are made and lost; some regions benefit at the expense of others. How these choices are made and how we think about that process are at the moral and political core of this work. The book is an important empirical source for understanding the building of information infrastructures.
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The Minimalist Program

Author: Noam Chomsky

Publisher: MIT Press

ISBN: 9780262531283

Category: Language Arts & Disciplines

Page: 420

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The Minimalist Program consists of four recent essays, including the previously unpublished 'Categories and Transformations, ' that attempt to situate linguistic theory in the broader cognitive sciences. In these essays the minimalist approach to linguistic theory is formulated and progressively developed.
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