Morphisms And Categories

Author : Jean Piaget,Gil Henriques,Edgar Ascher
Publisher : Psychology Press
Page : 290 pages
File Size : 51,8 Mb
Release : 2013-05-13
Category : Psychology
ISBN : 9781134743339

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Morphisms and Categories by Jean Piaget,Gil Henriques,Edgar Ascher Pdf

Despite dissent in many quarters, Piaget's epistemology and the developmental psychology derived from it remain the most powerful theories in either field. From the beginning, Piaget's fundamental epistemological notion was that all knowledge is rooted in action, and for a long time, he identified action with transformation. What is known is that which remains constant under transformatory action. This book represents a fundamental reformulation of that point of view. Alongside transformatory schemes, Piaget now presents evidence that nontransformatory actions -- comparisons that create morphisms and categories among diverse situations constitute a necessary and complementary instrument of knowledge. This work aims to elucidate that insight experimentally and theoretically and to understand the developmental interaction of comparing and transforming as knowledge is constructed. This first English translation of Piaget's work includes studies of children's understanding of geometric forms, machines, and abstract concepts. It contains a clear statement of his mature position on continuity with biology as well as with the history of ideas.

Author : Jean Piaget,Gil Henriques,Edgar Ascher
Publisher : Psychology Press
Page : 245 pages
File Size : 50,7 Mb
Release : 2013-05-13
Category : Psychology
ISBN : 9781134743261

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Morphisms and Categories by Jean Piaget,Gil Henriques,Edgar Ascher Pdf

Despite dissent in many quarters, Piaget's epistemology and the developmental psychology derived from it remain the most powerful theories in either field. From the beginning, Piaget's fundamental epistemological notion was that all knowledge is rooted in action, and for a long time, he identified action with transformation. What is known is that which remains constant under transformatory action. This book represents a fundamental reformulation of that point of view. Alongside transformatory schemes, Piaget now presents evidence that nontransformatory actions -- comparisons that create morphisms and categories among diverse situations constitute a necessary and complementary instrument of knowledge. This work aims to elucidate that insight experimentally and theoretically and to understand the developmental interaction of comparing and transforming as knowledge is constructed. This first English translation of Piaget's work includes studies of children's understanding of geometric forms, machines, and abstract concepts. It contains a clear statement of his mature position on continuity with biology as well as with the history of ideas.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 53,5 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

Introduction 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.

Author : David I. Spivak
Publisher : MIT Press
Page : 495 pages
File Size : 50,6 Mb
Release : 2014-10-17
Category : Mathematics
ISBN : 9780262320535

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Category Theory for the Sciences by David I. Spivak Pdf

An 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.

Author : Andrea Asperti,Giuseppe Longo
Publisher : MIT Press (MA)
Page : 330 pages
File Size : 42,9 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015022019742

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Categories, Types, and Structures by Andrea Asperti,Giuseppe Longo Pdf

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.

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 42,8 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9783540279501

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Categories and Sheaves by Masaki Kashiwara,Pierre Schapira Pdf

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Author : Birgit Richter
Publisher : Cambridge University Press
Page : 401 pages
File Size : 52,7 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108479622

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From Categories to Homotopy Theory by Birgit Richter Pdf

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 40,8 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608

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Sets for Mathematics by F. William Lawvere,Robert Rosebrugh Pdf

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Author : P. G. Romeo,Mikhail V. Volkov,A. R. Rajan
Publisher : Springer Nature
Page : 249 pages
File Size : 42,7 Mb
Release : 2021-03-26
Category : Mathematics
ISBN : 9789813348424

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Semigroups, Categories, and Partial Algebras by P. G. Romeo,Mikhail V. Volkov,A. R. Rajan Pdf

This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9–12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall’s relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.

Author : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 40,9 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107044241

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Basic Category Theory by Tom Leinster Pdf

A short introduction ideal for students learning category theory for the first time.

Author : J.W. Gray
Publisher : Springer
Page : 294 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540377689

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Formal Category Theory : Adjointness for 2-Categories by J.W. Gray Pdf

Author : Gregory Maxwell Kelly
Publisher : CUP Archive
Page : 260 pages
File Size : 47,9 Mb
Release : 1982-02-18
Category : Mathematics
ISBN : 0521287022

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Basic Concepts of Enriched Category Theory by Gregory Maxwell Kelly Pdf

Author : David E. Radford,David N. Yetter
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 40,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821827949

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Diagrammatic Morphisms and Applications by David E. Radford,David N. Yetter Pdf

The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely used in this capacity in many areas of algebra, low-dimensional topology and physics. It was also applied to problems in classical and quantum information processing and logic. This volume contains articles based on talks at the Special Session, ``Diagrammatic Morphisms in Algebra, Category Theory, and Topology'', at the AMS Sectional Meeting in San Francisco. The articles describe recent achievements in several aspects of diagrammatic morphisms and their applications. Some of them contain detailed expositions on various diagrammatic techniques. The introductory article by D. Yetter is a thorough account of the subject in a historical perspective.

Author : Dale Husemöller
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 51,8 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387215778

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Elliptic Curves by Dale Husemöller Pdf

First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices

Author : Steve Awodey
Publisher : Oxford University Press
Page : 328 pages
File Size : 48,7 Mb
Release : 2010-06-17
Category : Mathematics
ISBN : 9780199587360

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Category Theory by Steve Awodey Pdf

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.