Author : Jiri Adamek
Publisher :
Page : 0 pages
File Size : 45,17 MB
Release : 2009
Category : Categories (Mathematics)
ISBN : 9780486469348
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 : S. Eilenberg
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 23,25 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642999026
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 : Emily Riehl
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 21,36 MB
Release : 2017-03-09
Category : Mathematics
ISBN : 0486820807
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 : Horst Herrlich
Publisher : Addison Wesley Publishing Company
Page : 430 pages
File Size : 49,8 MB
Release : 1973
Category : Education
ISBN :
Author : Brendan Fong
Publisher : Cambridge University Press
Page : 351 pages
File Size : 26,39 MB
Release : 2019-07-18
Category : Mathematics
ISBN : 1108582249
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.
Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 38,32 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475747217
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 : Max Hailperin
Publisher : Max Hailperin
Page : 686 pages
File Size : 18,21 MB
Release : 1999
Category : Abstract data types (Computer science).
ISBN : 0534952119
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
Page : 300 pages
File Size : 35,67 MB
Release : 2008
Category : Capital
ISBN : 9788189833381
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
Page : 193 pages
File Size : 40,64 MB
Release : 2014-07-24
Category : Mathematics
ISBN : 1107044243
A short introduction ideal for students learning category theory for the first time.
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 782 pages
File Size : 47,76 MB
Release : 2022-02-10
Category : Mathematics
ISBN : 1108952194
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
