Category Structures
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Categories Types And Structures
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Author : Andrea Asperti
language : en
Publisher: MIT Press (MA)
Release Date : 1991
Categories Types And Structures written by Andrea Asperti and has been published by MIT Press (MA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.
Formal Category Theory Adjointness For 2 Categories
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Author : J.W. Gray
language : en
Publisher: Springer
Release Date : 2006-11-15
Formal Category Theory Adjointness For 2 Categories written by J.W. Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Categories In Algebra Geometry And Mathematical Physics
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Author : Alexei Davydov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Categories In Algebra Geometry And Mathematical Physics written by Alexei Davydov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Model Categories And Their Localizations
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Author : Philip S. Hirschhorn
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Model Categories And Their Localizations written by Philip S. Hirschhorn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces. A model category has a class of maps called weak equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the cofibrations and fibrations have extension and lifting properties similar to those of cofibration and fibration maps of topological spaces. During the past several decades the language of model categories has become standard in many areas of algebraic topology, and it is increasingly being used in other fields where homotopy theoretic ideas are becoming important, including modern algebraic $K$-theory and algebraic geometry. All these subjects and more are discussed in the book, beginning with the basic definitions and giving complete arguments in order to make the motivations and proofs accessible to the novice. The book is intended for graduate students and research mathematicians working in homotopy theory and related areas.
Early Category And Concept Development Making Sense Of The Blooming Buzzing Confusion
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Author : David H. Rakison Assistant Professor of Psychology Carnegie Mellon University
language : en
Publisher: Oxford University Press, USA
Release Date : 2003-01-09
Early Category And Concept Development Making Sense Of The Blooming Buzzing Confusion written by David H. Rakison Assistant Professor of Psychology Carnegie Mellon University and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-09 with Psychology categories.
Whether or not infants' earliest perception of the world is a "blooming, buzzing, confusion," it is not long before they come to perceive structure and order among the objects and events around them. At the core of this process, and cognitive development in general, is the ability to categorize--to group events, objects, or properties together--and to form mental representations, or concepts, that encapsulate the commonalities and structure of these categories. Categorization is the primary means of coding experience, underlying not only perceptual and reasoning processes, but also inductive inference and language. The aim of this book is to bring together the most recent findings and theories about the origins and early development of categorization and conceptual abilities. Despite recent advances in our understanding of this area, a number of hotly debated issues remain at the center of the controversy over categorization. Researchers continue to ask questions such as: Which mechanisms for categorization are available at birth and which emerge later? What are the relative roles of perceptual similarity and nonobservable properties in early classification? What is the role of contextual variation in categorization by infants and children? Do different experimental procedures reveal the same kind of knowledge? Can computational models simulate infant and child categorization? How do computational models inform behavioral research? What is the impact of language on category development? How does language partition the world? This book is the first to address these and other key cuestions within a single volume. The authors present a diverse set of views representing cutting-edge empirical and theoretical advances in the field. The result is a thorough review of empirical contributions to the literature, and a wealth of fresh theoretical perspectives on early categorization.
Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Categories For The Working Mathematician written by Saunders Mac Lane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Categories for the Working Mathematician provides 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. The book 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 characterized 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 two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.
The Psychology Of Word Meanings
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Author : Paula J. Schwanenflugel
language : en
Publisher: Psychology Press
Release Date : 2013-06-17
The Psychology Of Word Meanings written by Paula J. Schwanenflugel and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Language Arts & Disciplines categories.
This volume contains perspectives from a collection of cognitive scientists on the psychological, philosophical, and educational issues surrounding the meanings of words and how these meanings are learned and accessed. It features chapters covering the nature and structure of word meaning, how new word meanings are acquired in childhood and later on in life, and how research in word processing may tell us something about the way in which word meanings are represented and how they relate to the language processor.
A Handbook Of Model Categories
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Author : Scott Balchin
language : en
Publisher: Springer Nature
Release Date : 2021-10-29
A Handbook Of Model Categories written by Scott Balchin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-29 with Mathematics categories.
This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
Monoidal Category Theory
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05
Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
Higher Categories And Homotopical Algebra
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Author : Denis-Charles Cisinski
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Higher Categories And Homotopical Algebra written by Denis-Charles Cisinski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Mathematics categories.
At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.