Categories Allegories

Author : P.J. Freyd,A. Scedrov
Publisher : Elsevier
Page : 315 pages
File Size : 54,9 Mb
Release : 1990-11-08
Category : Mathematics
ISBN : 9780080887012

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Categories, Allegories by P.J. Freyd,A. Scedrov Pdf

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.

Author : R. Berghammer,Bernhard Möller,Georg Struth
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 55,5 Mb
Release : 2004-06-01
Category : Mathematics
ISBN : 9783540221456

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Relational and Kleene-Algebraic Methods in Computer Science by R. Berghammer,Bernhard Möller,Georg Struth Pdf

This book constitutes the thoroughly refereed joint postproceedings of the 7th International Seminar on Relational Methods in Computer Science and the 2nd International Workshop on Applications of Kleene Algebra held in Bad Malente, Germany in May 2003. The 21 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers address foundational and methodological aspects of the calculi of relations and Kleene algebra as well as applications of such methods in various areas of computer science and information processing.

Author : Michael Winter
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 45,6 Mb
Release : 2007-08-14
Category : Philosophy
ISBN : 9781402061646

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Goguen Categories by Michael Winter Pdf

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.

Author : Wolfram Kahl,Michael Winter,José Oliveira
Publisher : Springer
Page : 395 pages
File Size : 53,7 Mb
Release : 2015-09-24
Category : Mathematics
ISBN : 9783319247045

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Relational and Algebraic Methods in Computer Science by Wolfram Kahl,Michael Winter,José Oliveira Pdf

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.

Author : Grandis Marco
Publisher : World Scientific
Page : 536 pages
File Size : 40,6 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9789811205125

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Higher Dimensional Categories: From Double To Multiple Categories by Grandis Marco Pdf

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.

Author : Peter Höfner,Damien Pous,Georg Struth
Publisher : Springer
Page : 323 pages
File Size : 55,7 Mb
Release : 2017-05-08
Category : Mathematics
ISBN : 9783319574189

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Relational and Algebraic Methods in Computer Science by Peter Höfner,Damien Pous,Georg Struth Pdf

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.

Author : Harrie de Swart,Ewa Orlowska,Gunther Schmidt,Marc Roubens
Publisher : Springer
Page : 280 pages
File Size : 40,6 Mb
Release : 2004-01-30
Category : Computers
ISBN : 9783540246152

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Theory and Applications of Relational Structures as Knowledge Instruments by Harrie de Swart,Ewa Orlowska,Gunther Schmidt,Marc Roubens Pdf

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.

Author : Jose Luiz Fiadeiro
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 51,5 Mb
Release : 2005-08-09
Category : Computers
ISBN : 9783540268918

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Categories for Software Engineering by Jose Luiz Fiadeiro Pdf

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.

Author : Elaine M. Landry
Publisher : Oxford University Press
Page : 486 pages
File Size : 53,7 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198748991

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Categories for the Working Philosopher by Elaine M. Landry Pdf

This is the first book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is designed to show the interest and significant of category theory for philosophers working in a range of areas, including mathematics, proof theory, computer science, ontology, physics, biology, cognition, mathematical modelling, the structure of scientific theories, and the structure of the world. Moreover, it does this in a way that is accessible to non specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented fields, in a way that builds on the concepts already familiar to philosophers working in these areas. The book is split into two halves. The 'pure' chapters focus on the use of category theory for mathematical, foundational, and logical purposes, while the 'applied' chapters consider the use of category theory for representational purposes, investigating category theory as a framework for theories of physics and biology, for mathematical modelling more generally, and for the structure of scientific theories. Book jacket.

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 470 pages
File Size : 53,7 Mb
Release : 1994-11-03
Category : Mathematics
ISBN : 9780521441797

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Handbook of Categorical Algebra: Volume 2, Categories and Structures by Francis Borceux Pdf

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.

Author : Marco Grandis
Publisher : World Scientific
Page : 390 pages
File Size : 41,9 Mb
Release : 2021-03-05
Category : Mathematics
ISBN : 9789811236105

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Category Theory And Applications: A Textbook For Beginners (Second Edition) by Marco Grandis Pdf

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.

Author : Giandomenico Sica
Publisher : Polimetrica s.a.s.
Page : 292 pages
File Size : 52,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9788876990311

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What is Category Theory? by Giandomenico Sica Pdf

Author : Ana Agore
Publisher : Springer Nature
Page : 293 pages
File Size : 46,8 Mb
Release : 2024-01-13
Category : Mathematics
ISBN : 9783031428999

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A First Course in Category Theory by Ana Agore Pdf

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.

Author : Harrie de Swart
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 51,5 Mb
Release : 2011-05-20
Category : Computers
ISBN : 9783642210693

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Relational and Algebraic Methods in Computer Science by Harrie de Swart Pdf

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.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 42,9 Mb
Release : 2016-11-16
Category : Mathematics
ISBN : 9780486809038

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Category Theory in Context by Emily Riehl Pdf

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.