Download or read book Categories Allegories written by P.J. Freyd and published by Elsevier. This book was released on 1990-11-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.
Download or read book Categories Allegories written by Peter J. Freyd and published by North Holland. This book was released on 1990 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Goguen Categories written by Michael Winter and published by Springer Science & Business Media. This book was released on 2007-08-14 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations.
Download or read book Relational and Algebraic Methods in Computer Science written by Wolfram Kahl and published by Springer. This book was released on 2015-09-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 15th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2015, held in Braga, Portugal, in September/October 2015. The 20 revised full papers and 3 invited papers presented were carefully selected from 25 submissions. The papers deal with the theory of relation algebras and Kleene algebras, process algebras; fixed point calculi; idempotent semirings; quantales, allegories, and dynamic algebras; cylindric algebras, and about their application in areas such as verification, analysis and development of programs and algorithms, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics.
Download or read book Relational and Algebraic Methods in Computer Science written by Peter Höfner and published by Springer. This book was released on 2017-05-08 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2017, held in Lyon, France, in May 2017. The 17 revised full papers and 2 invited papers presented together with 1 invited abstract were carefully selected from 28 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Download or read book Higher Dimensional Categories From Double To Multiple Categories written by Grandis Marco and published by World Scientific. This book was released on 2019-09-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions.We want to show the advantages of this form for the theory of adjunctions and limits. Furthermore, this form is much simpler in higher dimension, starting with dimension three where weak 3-categories (also called tricategories) are already quite complicated, much more than weak or lax triple categories.This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories.
Download or read book Categories for the Working Philosopher written by Elaine M. Landry and published by Oxford University Press. This book was released on 2017 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Download or read book Theory and Applications of Relational Structures as Knowledge Instruments written by Harrie de Swart and published by Springer. This book was released on 2004-01-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relational structures abound in our daily environment: relational databases, data mining, scaling procedures, preference relations, etc. As the documentation of scientific results achieved within the European COST Action 274, TARSKI, this book advances the understanding of relational structures and the use of relational methods in various application fields. The 12 revised full papers were carefully reviewed and selected for presentations. The papers are devoted to mechanization of relational reasoning, relational scaling and preferences, and algebraic and logical foundations of real world relations.
Download or read book Categories in Computer Science and Logic written by John Walker Gray and published by American Mathematical Soc.. This book was released on 1989 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the proceedings of AMS-IMS-SIAM Summer Research Conference on Categories in Computer Science and Logic that was held at the University of Colorado in Boulder. This book discusses the use of category theory in formalizing aspects of computer programming and program design.
Download or read book Categories for Software Engineering written by Jose Luiz Fiadeiro and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates how category theory can be used for formal software development. The mathematical toolbox for the Software Engineering in the new age of complex interactive systems.
Download or read book Handbook of Categorical Algebra Volume 2 Categories and Structures written by Francis Borceux and published by Cambridge University Press. This book was released on 1994-11-03 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users.
Download or read book Category Theory And Applications A Textbook For Beginners Second Edition written by Marco Grandis and published by World Scientific. This book was released on 2021-03-05 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 better 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 the 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.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Download or read book Allegories of Transgression and Transformation written by Mary Beth Tierney-Tello and published by SUNY Press. This book was released on 1996-01-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the dynamic relationship between authority and gender in contemporary, experimental narrative works by four Latin American women writers: Diamela Eltit of Chile, Nelida Pinon of Brazil, Reina Roffe of Argentina, and Cristina Peri Rossi of Uruguay.
Download or read book What is Category Theory written by Giandomenico Sica and published by Polimetrica s.a.s.. This book was released on 2006 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relational and Algebraic Methods in Computer Science written by Harrie de Swart and published by Springer Science & Business Media. This book was released on 2011-05-20 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 12 International Conference on Relational and Algebraic Methods in Computer Science, RAMICS 2011, held in Rotterdam, The Netherlands, in May/June 2011. This conference merges the RelMICS (Relational Methods in Computer Science) and AKA (Applications of Kleene Algebra) conferences, which have been a main forum for researchers who use the calculus of relations and similar algebraic formalisms as methodological and conceptual tools. Relational and algebraic methods and software tools turn out to be useful for solving problems in social choice and game theory. For that reason this conference included a special track on Computational Social Choice and Social Software. The 18 papers included were carefully reviewed and selected from 27 submissions. In addition the volume contains 2 invited tutorials and 5 invited talks.
Download or read book A First Course in Category Theory written by Ana Agore and published by Springer Nature. This book was released on 2024-01-13 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to mastering its fundamental principles. Unlike traditional category theory books, which can often be overwhelming for beginners, this book has been carefully crafted to offer a clear and concise introduction to the subject. It covers all the essential topics, including categories, functors, natural transformations, duality, equivalence, (co)limits, and adjunctions. Abundant fully-worked examples guide readers in understanding the core concepts, while complete proofs and instructive exercises reinforce comprehension and promote self-study. The author also provides background material and references, making the book suitable for those with a basic understanding of groups, rings, modules, topological spaces, and set theory. Based on the author's course at the Vrije Universiteit Brussel, the book is perfectly suited for classroom use in a first introductory course in category theory. Its clear and concise style, coupled with its detailed coverage of key concepts, makes it equally suited for self-study.
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2016-11-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester course on 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, 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. Prerequisites are limited to familiarity with some basic set theory and logic.
