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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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.
The Theory of Categories
Author: F.C. Brentano
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 367
ISBN-13: 9400981899
DOWNLOAD EBOOKThis book contains the definitive statement of Franz Brentano's views on meta physics. It is made up of essays which were dictated by Brentano during the last ten years of his life, between 1907 and 1917. These dictations were assembled and edited by Alfred Kastil and first published by the Felix Meiner Verlag in 1933 under the title Kategorienlehre. Kastil added copious notes to Brentano's text. These notes have been included, with some slight omissions, in the present edition; the bibliographical references have been brought up to date. Brentano's approach to philosophy is unfamiliar to many contemporay readers. I shall discuss below certain fundamental points which such readers are likely to find the most difficult. I believe that once these points are properly understood, then what Brentano has to say will be seen to be of first importance to philosophy. THE PRIMACY OF THE INTENTIONAL To understand Brentano's theory of being, one must realize that he appeals to what he calls inner perception for his paradigmatic uses of the word "is". For inner perception, according to Brentano, is the source of our knowledge of the nature of being, just as it is the source of our knowledge of the nature of truth and of the nature of good and evil. And what can be said about the being of things that are not apprehended in inner perception can be understood only by analogy with what we are able to say about ourselves as thinking subjects.
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.
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.
CATEGORIES
Author: Aristotle
Publisher: YouHui Culture Publishing Company
Published: 2001
Total Pages: 61
ISBN-13:
DOWNLOAD EBOOKCATEGORIES by Aristotle translated by E. M. Edghill 1 Things are said to be named 'equivocally' when, though they have a common name, the definition corresponding with the name differs for each. Thus, a real man and a figure in a picture can both lay claim to the name 'animal'; yet these are equivocally so named, for, though they have a common name, the definition corresponding with the name differs for each. For should any one define in what sense each is an animal, his definition in the one case will be appropriate to that case only. On the other hand, things are said to be named 'univocally' which have both the name and the definition answering to the name in common. A man and an ox are both 'animal', and these are univocally so named, inasmuch as not only the name, but also the definition, is the same in both cases: for if a man should state in what sense each is an animal, the statement in the one case would be identical with that in the other. Things are said to be named 'derivatively', which derive their name from some other name, but differ from it in termination. Thus the grammarian derives his name from the word 'grammar', and the courageous man from the word 'courage'.
Theory of Categories
Author:
Publisher: Academic Press
Published: 1965-01-01
Total Pages: 291
ISBN-13: 0080873294
DOWNLOAD EBOOKTheory of Categories
An Introduction to the Language of Category Theory
Author: Steven Roman
Publisher: Birkhäuser
Published: 2017-01-05
Total Pages: 174
ISBN-13: 331941917X
DOWNLOAD EBOOKThis 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.
Diagrammatic Immanence
Author: Rocco Gangle
Publisher: Edinburgh University Press
Published: 2016-08-18
Total Pages: 264
ISBN-13: 1474404200
DOWNLOAD EBOOKA renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.
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.
