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Abstract and Concrete Categories by Jiri Adamek,Horst Herrlich,George E. Strecker Pdf
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.
Abstract and Concrete Categories by Jiri Adamek,Horst Herrlich,George E. Strecker Pdf
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.
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.
Proceedings of the Conference on Categorical Algebra by S. Eilenberg,D. K. Harrison,H. Röhrl,S. MacLane Pdf
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.
The Dialectics of the Abstract and the Concrete in Marx's Capital by E. V. Ilyenkov Pdf
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
Concrete Abstractions by Max Hailperin,Barbara Kaiser,Karl Knight Pdf
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.
Categories for the Working Mathematician by Saunders Mac Lane Pdf
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 Approach to Abstract Algebra by W. W. Sawyer Pdf
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.
Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Categories, Types, and Structures by Andrea Asperti,Giuseppe Longo Pdf
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.
Relations: Concrete, Abstract, And Applied - An Introduction by Herbert Toth Pdf
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: