Search results for: basic-category-theory-for-computer-scientists

Basic Category Theory for Computer Scientists

Author : Benjamin C. Pierce
File Size : 39.59 MB
Format : PDF, ePub
Download : 358
Read : 1208
Download »
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

Basic Category Theory for Computer Scientists

Author : Benjamin C. Pierce
File Size : 78.71 MB
Format : PDF, ePub, Docs
Download : 149
Read : 712
Download »
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

A Taste of Category Theory for Computer Scientists

Author : Benjamin C. Pierce
File Size : 56.32 MB
Format : PDF, ePub
Download : 340
Read : 1297
Download »
Abstract: "Category theory is a branch of pure mathematics that more and more frequently touches the daily work of computer scientists, especially those with an interest in programming languages or formal specifications. This survey is an 'introduction to the introductions' to category theory--a brief answer to the questions, 'What is category theory?' 'What are its basic concepts?' 'What are computer scientists using it for?' and 'Where can I learn more?' The first section introduces the most common category-theoretic terms and idioms, assuming as little specific mathematical background as possible. the second section presents four case studies from the recent research literature applying category theory to the semantics of computation. A reading list in the third section suggests pathways into the existing literature, including textbooks, standard reference works, and selected research papers."

Category Theory for Computing Science

Author : Michael Barr
File Size : 42.66 MB
Format : PDF, ePub
Download : 411
Read : 293
Download »
Textbook for advanced undergraduates, graduates and researchers in computing science and mathematics expounds the basic ideas and construction of category theory, with examples from and applications to computing science. The emphasis is on examples and on understanding the concepts rather than on formal proofs of the theorems. Annotation copyright.

Basic Category Theory

Author : Tom Leinster
File Size : 38.89 MB
Format : PDF, ePub
Download : 798
Read : 1241
Download »
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.

Computer Science

Author :
File Size : 83.94 MB
Format : PDF, ePub
Download : 196
Read : 237
Download »

Category Theory And Applications A Textbook For Beginners Second Edition

Author : Marco Grandis
File Size : 80.31 MB
Format : PDF, Docs
Download : 362
Read : 621
Download »
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

An Introduction to the Language of Category Theory

Author : Steven Roman
File Size : 78.92 MB
Format : PDF, Mobi
Download : 219
Read : 295
Download »
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.

A New Foundation for Representation in Cognitive and Brain Science

Author : Jaime Gómez-Ramirez
File Size : 46.68 MB
Format : PDF, ePub
Download : 570
Read : 795
Download »
The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

Computational Science ICCS 2007

Author : Yong Shi
File Size : 89.97 MB
Format : PDF
Download : 400
Read : 657
Download »
Part of a four-volume set, this book constitutes the refereed proceedings of the 7th International Conference on Computational Science, ICCS 2007, held in Beijing, China in May 2007. The papers cover a large volume of topics in computational science and related areas, from multiscale physics to wireless networks, and from graph theory to tools for program development.