Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Abstract and Concrete Categories PDF full book. Access full book title Abstract and Concrete Categories by Jiri Adamek. Download full books in PDF and EPUB format.
Author: Jiri Adamek Publisher: Wiley-Interscience ISBN: Category : Mathematics Languages : en Pages : 504
Book Description
A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.
Author: Jiri Adamek Publisher: Wiley-Interscience ISBN: Category : Mathematics Languages : en Pages : 504
Book Description
A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.
Author: Emily Riehl Publisher: Courier Dover Publications ISBN: 0486820807 Category : Mathematics Languages : en Pages : 273
Book Description
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 ISBN: 3642999026 Category : Mathematics Languages : en Pages : 571
Book Description
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: Max Hailperin Publisher: Max Hailperin ISBN: 0534952119 Category : Abstract data types (Computer science). Languages : en Pages : 686
Book Description
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 ISBN: 9788189833381 Category : Capital Languages : en Pages : 300
Book Description
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: Benjamin C. Pierce Publisher: MIT Press ISBN: 0262326450 Category : Computers Languages : en Pages : 117
Book Description
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
Author: W. W. Sawyer Publisher: Courier Dover Publications ISBN: 0486824616 Category : Mathematics Languages : en Pages : 241
Book Description
Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.
Author: Herbert Toth Publisher: World Scientific ISBN: 9811220360 Category : Mathematics Languages : en Pages : 573
Book Description
The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
Author: Saunders Mac Lane Publisher: Springer Science & Business Media ISBN: 1475747217 Category : Mathematics Languages : en Pages : 320
Book Description
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: Jiri Adamek
Author: Jiri Adamek
Author: Emily Riehl
Author: S. Eilenberg
Author: Horst Herrlich
Author: Max Hailperin
Author: E. V. Ilyenkov
Author: Benjamin C. Pierce
Author: W. W. Sawyer
Author: Herbert Toth
Author: Saunders Mac Lane