Abstract and Concrete Categories

Abstract and Concrete Categories

Author: Jiri Adamek

Publisher:

Published: 2009

Total Pages: 0

ISBN-13: 9780486469348

DOWNLOAD EBOOK

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.


Proceedings of the Conference on Categorical Algebra

Proceedings of the Conference on Categorical Algebra

Author: S. Eilenberg

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 571

ISBN-13: 3642999026

DOWNLOAD EBOOK

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.


Category Theory in Context

Category Theory in Context

Author: Emily Riehl

Publisher: Courier Dover Publications

Published: 2017-03-09

Total Pages: 273

ISBN-13: 0486820807

DOWNLOAD EBOOK

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.


An Invitation to Applied Category Theory

An Invitation to Applied Category Theory

Author: Brendan Fong

Publisher: Cambridge University Press

Published: 2019-07-18

Total Pages: 351

ISBN-13: 1108582249

DOWNLOAD EBOOK

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.


Categories for the Working Mathematician

Categories for the Working Mathematician

Author: Saunders Mac Lane

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 320

ISBN-13: 1475747217

DOWNLOAD EBOOK

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.


Concrete Abstractions

Concrete Abstractions

Author: Max Hailperin

Publisher: Max Hailperin

Published: 1999

Total Pages: 686

ISBN-13: 0534952119

DOWNLOAD EBOOK

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.


The Dialectics of the Abstract and the Concrete in Marx's Capital

The Dialectics of the Abstract and the Concrete in Marx's Capital

Author: E. V. Ilyenkov

Publisher: Aakar Books

Published: 2008

Total Pages: 300

ISBN-13: 9788189833381

DOWNLOAD EBOOK

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


Basic Category Theory

Basic Category Theory

Author: Tom Leinster

Publisher: Cambridge University Press

Published: 2014-07-24

Total Pages: 193

ISBN-13: 1107044243

DOWNLOAD EBOOK

A short introduction ideal for students learning category theory for the first time.


Language, Mind and Body

Language, Mind and Body

Author: John E. Joseph

Publisher: Cambridge University Press

Published: 2018

Total Pages: 293

ISBN-13: 110714955X

DOWNLOAD EBOOK

Where is language? Centuries of efforts to 'incorporate' language lie behind current concepts of extended mind and embodied cognition. This book examines this question.