Abstract And Concrete Categories
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Author |
: Jiri Adamek |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2009 |
ISBN-10 |
: 0486469344 |
ISBN-13 |
: 9780486469348 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Abstract and Concrete Categories by : Jiri Adamek
This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.
Author |
: Emily Riehl |
Publisher |
: Courier Dover Publications |
Total Pages |
: 273 |
Release |
: 2017-03-09 |
ISBN-10 |
: 9780486820804 |
ISBN-13 |
: 0486820807 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Category Theory in Context by : Emily Riehl
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.
Author |
: S. Eilenberg |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 571 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642999024 |
ISBN-13 |
: 3642999026 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Proceedings of the Conference on Categorical Algebra by : S. Eilenberg
This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7-12,1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of Scientific Research. Of the thirty-seven mathemati cians, who were present seventeen presented their papers in the form of lectures. In addition, this volume contains papers contributed by other attending participants as well as by those who, after having planned to attend, were unable to do so. The editors hope to have achieved a representative, if incomplete, cover age of the present activities in Categorical Algebra within the United States by bringing together this group of mathematicians and by solici ting the articles contained in this volume. They also hope that these Proceedings indicate the trend of research in Categorical Algebra in this country. In conclusion, the editors wish to thank the participants and contrib. utors to these Proceedings for their continuous cooperation and encour agement. Our thanks are also due to the Springer-Verlag for publishing these Proceedings in a surprisingly short time after receiving the manu scripts.
Author |
: Saunders Mac Lane |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 320 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9781475747218 |
ISBN-13 |
: 1475747217 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Categories for the Working Mathematician by : Saunders Mac Lane
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author |
: Horst Herrlich |
Publisher |
: Addison Wesley Publishing Company |
Total Pages |
: 430 |
Release |
: 1973 |
ISBN-10 |
: STANFORD:36105031398253 |
ISBN-13 |
: |
Rating |
: 4/5 (53 Downloads) |
Synopsis Category Theory by : Horst Herrlich
Author |
: Brendan Fong |
Publisher |
: Cambridge University Press |
Total Pages |
: 351 |
Release |
: 2019-07-18 |
ISBN-10 |
: 9781108482295 |
ISBN-13 |
: 1108482295 |
Rating |
: 4/5 (95 Downloads) |
Synopsis An Invitation to Applied Category Theory by : Brendan Fong
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Author |
: Max Hailperin |
Publisher |
: Max Hailperin |
Total Pages |
: 686 |
Release |
: 1999 |
ISBN-10 |
: 9780534952112 |
ISBN-13 |
: 0534952119 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Concrete Abstractions by : Max Hailperin
CONCRETE ABSTRACTIONS offers students a hands-on, abstraction-based experience of thinking like a computer scientist. This text covers the basics of programming and data structures, and gives first-time computer science students the opportunity to not only write programs, but to prove theorems and analyze algorithms as well. Students learn a variety of programming styles, including functional programming, assembly-language programming, and object-oriented programming (OOP). While most of the book uses the Scheme programming language, Java is introduced at the end as a second example of an OOP system and to demonstrate concepts of concurrent programming.
Author |
: E. V. Ilyenkov |
Publisher |
: Aakar Books |
Total Pages |
: 300 |
Release |
: 2008 |
ISBN-10 |
: 8189833383 |
ISBN-13 |
: 9788189833381 |
Rating |
: 4/5 (83 Downloads) |
Synopsis The Dialectics of the Abstract and the Concrete in Marx's Capital by : E. V. Ilyenkov
The book presents an integral Marxist conception of the dialectics and methodology of scientific theoretical cognition, of the dialectical interrelation between the abstract and the concrete, of the unity of the historical and the logical, of the correlat
Author |
: Tom Leinster |
Publisher |
: Cambridge University Press |
Total Pages |
: 193 |
Release |
: 2014-07-24 |
ISBN-10 |
: 9781107044241 |
ISBN-13 |
: 1107044243 |
Rating |
: 4/5 (41 Downloads) |
Synopsis Basic Category Theory by : Tom Leinster
A short introduction ideal for students learning category theory for the first time.
Author |
: Benjamin C. Pierce |
Publisher |
: MIT Press |
Total Pages |
: 117 |
Release |
: 1991-08-07 |
ISBN-10 |
: 9780262326452 |
ISBN-13 |
: 0262326450 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
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