Basic Category Theory
Author: Tom Leinster
Publisher: Cambridge University Press
Published: 2014-07-24
Total Pages: 193
ISBN-13: 1107044243
DOWNLOAD EBOOKA short introduction ideal for students learning category theory for the first time.
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Basic Category Theory for Computer Scientists
Author: Benjamin C. Pierce
Publisher: MIT Press
Published: 1991-08-07
Total Pages: 117
ISBN-13: 0262326450
DOWNLOAD EBOOKBasic 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
Category Theory in Context
Author: Emily Riehl
Publisher: Courier Dover Publications
Published: 2017-03-09
Total Pages: 273
ISBN-13: 0486820807
DOWNLOAD EBOOKIntroduction 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.
Basic Concepts of Enriched Category Theory
Author: Gregory Maxwell Kelly
Publisher: CUP Archive
Published: 1982-02-18
Total Pages: 260
ISBN-13: 9780521287029
DOWNLOAD EBOOKCategories for the Working Mathematician
Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 320
ISBN-13: 1475747217
DOWNLOAD EBOOKAn 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.
An Introduction to Category Theory
Author: Harold Simmons
Publisher: Cambridge University Press
Published: 2011-09-22
Total Pages: 237
ISBN-13: 1139503324
DOWNLOAD EBOOKCategory 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.
2-Dimensional Categories
Author: Niles Johnson
Publisher: Oxford University Press, USA
Published: 2021-01-31
Total Pages: 636
ISBN-13: 0198871376
DOWNLOAD EBOOK2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
An Invitation to Applied Category Theory
Author: Brendan Fong
Publisher: Cambridge University Press
Published: 2019-07-18
Total Pages: 351
ISBN-13: 1108582249
DOWNLOAD EBOOKCategory 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.
Category Theory
Author: Steve Awodey
Publisher: Oxford University Press
Published: 2010-06-17
Total Pages: 328
ISBN-13: 0199587361
DOWNLOAD EBOOKA comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.
Category Theory for the Sciences
Author: David I. Spivak
Publisher: MIT Press
Published: 2014-10-17
Total Pages: 495
ISBN-13: 0262320533
DOWNLOAD EBOOKAn introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. 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.
