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Topology and Category Theory in Computer Science

Topology and Category Theory in Computer Science Author George M. Reed
ISBN-10 9780198537601
Release 1991
Pages 390
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This work consists of a selection of papers from the proceedings of a special session on topology and category theory in computer science, held at The Oxford Topology Symposium in June 1989. The session achieved a mixing of ideas between the two communities - giving one a course of new problems with a more practical flavour, and the other a source of solutions and ideas.

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.

Categorical Methods in Computer Science

Categorical Methods in Computer Science Author Hartmut Ehrig
ISBN-10 3540517227
Release 1989-10-11
Pages 354
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This volume contains selected papers of the International Workshop on "Categorical Methods in Computer Science - with Aspects from Topology" and of the "6th International Data Type Workshop" held in August/September 1988 in Berlin. The 23 papers of this volume are grouped into three parts: Part 1 includes papers on categorical foundations and fundamental concepts from category theory in computer science. Part 2 presents applications of categorical methods to algebraic specification languages and techniques, data types, data bases, programming, and process specifications. Part 3 comprises papers on categorial aspects from topology which mainly concentrate on special adjoint situations like cartesian closeness, Galois connections, reflections, and coreflections which are of growing interest in categorical topology and computer science.

Category Theory and Applications

Category Theory and Applications Author Marco Grandis
ISBN-10 9789813231085
Release 2018-01-16
Pages 304
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Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots. This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications. Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields. Contents: Introduction Categories, Functors and Natural Transformations Limits and Colimits Adjunctions and Monads Applications in Algebra Applications in Topology and Algebraic Topology Applications in Homological Algebra Hints at Higher Dimensional Category Theory References Indices Readership: Graduate students and researchers of mathematics, computer science, physics. Keywords: Category TheoryReview: Key Features: The main notions of Category Theory are presented in a concrete way, starting from examples taken from the elementary part of well-known disciplines: Algebra, Lattice Theory and Topology The theory is developed presenting other examples and some 300 exercises; the latter are endowed with a solution, or a partial solution, or adequate hints Three chapters and some extra sections are devoted to applications

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.

Algebra Topology and Category Theory

Algebra  Topology  and Category Theory Author Alex Heller
ISBN-10 9781483262611
Release 2014-05-10
Pages 238
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Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.

Category Theory

Category Theory Author Horst Herrlich
ISBN-10 UCSD:31822000257279
Release 1979
Pages 400
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Category Theory has been writing in one form or another for most of life. You can find so many inspiration from Category Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Category Theory book for free.

An Introduction to Category Theory

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

Coherence in Three Dimensional Category Theory

Coherence in Three Dimensional Category Theory Author Nick Gurski
ISBN-10 9781107034891
Release 2013-03-21
Pages 278
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Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.

Computational Category Theory

Computational Category Theory Author D. David E. Rydeheard
ISBN-10 UOM:39015013476752
Release 1988
Pages 257
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Computational Category Theory has been writing in one form or another for most of life. You can find so many inspiration from Computational Category Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Computational Category Theory book for free.

Tool and Object

Tool and Object Author Ralph Krömer
ISBN-10 9783764375249
Release 2007-06-25
Pages 367
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Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Category Theory and Computer Science

Category Theory and Computer Science Author Eugenio Moggi
ISBN-10 354063455X
Release 1997-08-20
Pages 319
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This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.

Combinatorial Algebraic Topology

Combinatorial Algebraic Topology Author Dimitry Kozlov
ISBN-10 9783540719625
Release 2007-12-29
Pages 390
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This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Category Theory for the Sciences

Category Theory for the Sciences Author David I. Spivak
ISBN-10 9780262320535
Release 2014-10-17
Pages 496
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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 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.

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.

Nonabelian Algebraic Topology

Nonabelian Algebraic Topology Author Ronald Brown
ISBN-10 3037190833
Release 2011
Pages 668
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Nonabelian Algebraic Topology has been writing in one form or another for most of life. You can find so many inspiration from Nonabelian Algebraic Topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Nonabelian Algebraic Topology book for free.