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Conceptual Mathematics

Conceptual Mathematics Author F. William Lawvere
ISBN-10 9781139643962
Release 2009-07-30
Pages
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In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.



Conceptual Mathematics

Conceptual Mathematics Author F. William Lawvere
ISBN-10 9780521894852
Release 2009-07-30
Pages 390
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In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.



Conceptual Mathematics

Conceptual Mathematics Author F. William Lawvere
ISBN-10 0521478170
Release 1997-10-09
Pages 358
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This is an introduction to thinking about elementary mathematics from a categorial point of view. The goal is to explore the consequences of a new and fundamental insight about the nature of mathematics.



Categories for the Working Mathematician

Categories for the Working Mathematician Author Saunders Mac Lane
ISBN-10 9781475747218
Release 2013-04-17
Pages 317
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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.



Sets for Mathematics

Sets for Mathematics Author F. William Lawvere
ISBN-10 0521010608
Release 2003-01-27
Pages 261
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In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.



An Introduction to Category Theory

An Introduction to Category Theory Author Harold Simmons
ISBN-10 9781139503327
Release 2011-09-22
Pages
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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.



Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists Author Benjamin C. Pierce
ISBN-10 0262660717
Release 1991
Pages 100
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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.



Category Theory

Category Theory Author Steve Awodey
ISBN-10 9780191612558
Release 2010-06-17
Pages 328
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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.



Introduction to Higher Order Categorical Logic

Introduction to Higher Order Categorical Logic Author J. Lambek
ISBN-10 0521356539
Release 1988-03-25
Pages 304
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Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.



Topology Via Logic

Topology Via Logic Author Steven Vickers
ISBN-10 0521576512
Release 1996-08-22
Pages 200
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This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.



Introduction to Combinators and lambda Calculus

Introduction to Combinators and  lambda  Calculus Author J. R. Hindley
ISBN-10 0521268966
Release 1986-05-29
Pages 360
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Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.



Conceptual Mathematics A First Introduction to Categories

Conceptual Mathematics  A First Introduction to Categories Author CTI Reviews
ISBN-10 9781467243841
Release 2016-10-16
Pages 23
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Facts101 is your complete guide to Conceptual Mathematics, A First Introduction to Categories. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.



Abstract and Concrete Categories

Abstract and Concrete Categories Author Jiri Adamek
ISBN-10 0486469344
Release 2009-01-01
Pages 517
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This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.



Basic Category Theory

Basic Category Theory Author Tom Leinster
ISBN-10 9781107044241
Release 2014-07-24
Pages 190
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A short introduction ideal for students learning category theory for the first time.



Mathematics Form and Function

Mathematics Form and Function Author Saunders MacLane
ISBN-10 9781461248729
Release 2012-12-06
Pages 476
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Mathematics Form and Function has been writing in one form or another for most of life. You can find so many inspiration from Mathematics Form and Function also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics Form and Function book for free.



Category Theory in Context

Category Theory in Context Author Emily Riehl
ISBN-10 9780486820804
Release 2017-03-09
Pages 272
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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.



A Book of Abstract Algebra

A Book of Abstract Algebra Author Charles C Pinter
ISBN-10 9780486474175
Release 2010-01-14
Pages 384
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.