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1. Category Theory in Context (Aurora: Dover Modern Math Originals) by Emily Riehl
Product Description Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a onesemester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. While the reader will be rewarded for familiarity with these background mathematical contexts, essential prerequisites are limited to basic set theory and logic.
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2. Category Theory for the Sciences (MIT Press) by David I. Spivak
Product Description 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 nonmathematicians. 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.
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3. Category Theory (Oxford Logic Guides) by Steve Awodey
Product Description 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.
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Similar Items: 1. Categories for the Working Mathematician (Graduate Texts in Mathematics) 2. Category Theory for the Sciences (MIT Press) 3. Conceptual Mathematics: A First Introduction to Categories 4. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 5. Category Theory in Context (Aurora: Dover Modern Math Originals) 6. An Introduction to Category Theory 7. Types and Programming Languages (MIT Press) 8. Basic Category Theory for Computer Scientists (Foundations of Computing) 9. Purely Functional Data Structures 10. Basic Category Theory (Cambridge Studies in Advanced Mathematics) . 
4. An Introduction to the Language of Category Theory (Compact Textbooks in Mathematics) by Steven Roman
Product Description 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 universitylevel 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, stepbystep 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 homset categories. Chapter 2 is devoted to functors and natural transformations, 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.
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5. Categories for the Working Mathematician (Graduate Texts in Mathematics) by Saunders Mac Lane
Product Description 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 adjointlike 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 2categories and the higher dimensional categories which have recently come into prominence.
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Similar Items: 1. Category Theory (Oxford Logic Guides) 2. Conceptual Mathematics: A First Introduction to Categories 3. Category Theory for the Sciences (MIT Press) 4. Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext) 5. Algebraic Topology 6. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 7. Algebraic Geometry (Graduate Texts in Mathematics) 8. Purely Functional Data Structures 9. Algebra: Chapter 0 (Graduate Studies in Mathematics) 10. A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series) . 
6. An Introduction to Category Theory by Harold Simmons
Product Description 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, easytoread 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 selfstudy. It can also be used as a recommended text for a taught introductory course.
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Similar Items: 1. Category Theory for the Sciences (MIT Press) 2. Category Theory (Oxford Logic Guides) 3. Category Theory in Context (Aurora: Dover Modern Math Originals) 4. Basic Category Theory (Cambridge Studies in Advanced Mathematics) 5. Conceptual Mathematics: A First Introduction to Categories 6. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 7. An Introduction to the Language of Category Theory (Compact Textbooks in Mathematics) 8. Deep Learning (Adaptive Computation and Machine Learning series) 9. Book of Proof 10. Categories for the Working Mathematician (Graduate Texts in Mathematics) . 
7. Basic Category Theory (Cambridge Studies in Advanced Mathematics) by Tom Leinster
Product Description 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.
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8. Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce
Product Description 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. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University.Contents : Tutorial. Applications. Further Reading.
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Similar Items: 1. Types and Programming Languages (MIT Press) 2. Purely Functional Data Structures 3. An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) 4. Category Theory (Oxford Logic Guides) 5. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics) 6. The Little Prover (MIT Press) 7. Category Theory for the Sciences (MIT Press) 8. Advanced Topics in Types and Programming Languages (MIT Press) 9. Structure and Interpretation of Computer Programs  2nd Edition (MIT Electrical Engineering and Computer Science) 10. Book of Proof . 
9. How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics by Eugenia Cheng
Product Description What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cuttingedge mathematics of mathematics,” that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.
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10. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics) by Charles C Pinter
Product Description Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easytoread treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior and seniorlevel math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definitiontheoremproofcorollaryexample; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.
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Similar Items: 1. Introduction to Topology: Third Edition (Dover Books on Mathematics) 2. Number Theory (Dover Books on Mathematics) 3. Introduction to Graph Theory (Dover Books on Mathematics) 4. A Book of Set Theory (Dover Books on Mathematics) 5. Linear Algebra (Dover Books on Mathematics) 6. An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics) 7. Fourier Series (Dover Books on Mathematics) 8. Introduction to Analysis (Dover Books on Mathematics) 9. Probability Theory: A Concise Course (Dover Books on Mathematics) 10. Book of Proof . 
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