Category Book PDF, EPUB Download & Read Online Free


Category Theory

Category Theory
Author: Steve Awodey
Publisher: Oxford University Press
ISBN: 0191513822
Pages: 256
Year: 2006-05
View: 617
Read: 939

This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads.

Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists
Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262660717
Pages: 100
Year: 1991
View: 797
Read: 953

Basic Category Theory for Computer Scientists provides a straightforward presentationof the basic constructions and terminology of category theory, including limits, functors, naturaltransformations, adjoints, and cartesian closed categories.

What is Category Theory?

What is Category Theory?
Author: Giandomenico Sica
Publisher: Polimetrica s.a.s.
ISBN: 8876990313
Pages: 290
Year: 2006-01-01
View: 423
Read: 1051

Category Theory for the Sciences

Category Theory for the Sciences
Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262320533
Pages: 496
Year: 2014-10-17
View: 390
Read: 154

Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs -- categories in disguise. After explaining the "big three" concepts of category theory -- categories, functors, and natural transformations -- the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

Categories and Computer Science

Categories and Computer Science
Author: R. F. C. Walters
Publisher: Cambridge University Press
ISBN: 0521422264
Pages: 166
Year: 1991
View: 462
Read: 1020

Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.

The Category of the Person

The Category of the Person
Author: Michael Carrithers, Steven Collins, Steven Lukes
Publisher: Cambridge University Press
ISBN: 0521277574
Pages: 309
Year: 1985-12-27
View: 1245
Read: 756

The concept that people have of themselves as a 'person' is one of the most intimate notions that they hold. Yet the way in which the category of the person is conceived varies over time and space. In this volume, anthropologists, philosophers, and historians examine the notion of the person in different cultures, past and present. Taking as their starting point a lecture on the person as a category of the human mind, given by Marcel Mauss in 1938, the contributors critically assess Mauss's speculation that notions of the person, rather than being primarily philosophical or psychological, have a complex social and ideological origin. Discussing societies ranging from ancient Greece, India, and China to modern Africa and Papua New Guinea, they provide fascinating descriptions of how these different cultures define the person. But they also raise deeper theoretical issues: What is universally constant and what is culturally variable in people's thinking about the person? How can these variations be explained? Has there been a general progressive development toward the modern Western view of the person? What is distinctive about this? How do one's notions of the person inform one's ability to comprehend alternative formulations? These questions are of compelling interest for a wide range of anthropologists, philosophers, historians, psychologists, sociologists, orientalists, and classicists. The book will appeal to any reader concerned with understanding one of the most fundamental aspects of human existence.

Category

Category
Author: Edward Gorey
Publisher: Pomegranate
ISBN: 0764937502
Pages: 112
Year: 2006-08-01
View: 337
Read: 1283

Finally, back in print! Edward Gorey's CATEGORY was first published by Gotham Book Mart in 1974. The English language edition has been out of print for decades. One of Gorey's most beloved books, CATEGORY collects a series of fifty cat vignettes, originally created by the artist as accompaniments to a limited edition of his book Amphigorey. Gorey once said, "I can't conceive of a life without cats." Now Gorey fans and cat lovers alike won't have to conceive of a world without CATEGOREY. Edward Gorey (1925-2000) may be best known for his mildly unsettling illustrated tales and cautionary alphabets—The Deranged Cousins, The Gashlycrumb Tinies, and The Doubtful Guest, among many others. He was also a playwright, an award-winning set and costume designer, and the creator of the animated introductions to the PBS series Mystery!

Category Theory in Context

Category Theory in Context
Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Pages: 272
Year: 2017-03-09
View: 931
Read: 1198

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 Introduction to the Language of Category Theory

An Introduction to the Language of Category Theory
Author: Steven Roman
Publisher: Birkhäuser
ISBN: 331941917X
Pages: 169
Year: 2017-02-20
View: 606
Read: 384

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.

Category Theory

Category Theory
Author: Steve Awodey
Publisher: OUP Oxford
ISBN: 0191612553
Pages: 328
Year: 2010-06-17
View: 569
Read: 975

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

Categories for Types

Categories for Types
Author: Roy L. Crole
Publisher: Cambridge University Press
ISBN: 0521457017
Pages: 335
Year: 1993
View: 967
Read: 889

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.

Basic Category Theory

Basic Category Theory
Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Pages: 190
Year: 2014-07-24
View: 775
Read: 554

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

Aristotle on the Category of Relation

Aristotle on the Category of Relation
Author: Pamela Michelle Hood
Publisher: University Press of America
ISBN: 0761830073
Pages: 154
Year: 2004
View: 580
Read: 357

In Aristotle on the Category of Relation, Pamela Hood challenges the view that Aristotle's conception of relation is so divergent from our own that it does not count as a theory of relation at all. This book presents compelling evidence that Aristotle's theory of relation is more robust than originally suspected.

An Introduction to Category Theory

An Introduction to Category Theory
Author: Harold Simmons
Publisher: Cambridge University Press
ISBN: 1139503324
Pages:
Year: 2011-09-22
View: 486
Read: 1164

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.

Handbook of Categorical Algebra: Volume 1, Basic Category Theory

Handbook of Categorical Algebra: Volume 1, Basic Category Theory
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 0521441781
Pages: 345
Year: 1994-08-26
View: 552
Read: 1120

The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.

Recent Post