Algebraic Theories

Algebraic Theories
Author :
Publisher : Springer Science & Business Media
Total Pages : 364
Release :
ISBN-10 : 9781461298601
ISBN-13 : 1461298601
Rating : 4/5 (601 Downloads)

Book Synopsis Algebraic Theories by : E.G. Manes

Download or read book Algebraic Theories written by E.G. Manes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, category theory has widened its scope and now inter acts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chap ter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathe maticians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book.


Algebraic Theories Related Books

Algebraic Theories
Language: en
Pages: 364
Authors: E.G. Manes
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

In the past decade, category theory has widened its scope and now inter acts with many areas of mathematics. This book develops some of the interactions between
Algebraic Theories
Language: en
Pages: 241
Authors: Leonard Dickson
Categories: Mathematics
Type: BOOK - Published: 2014-03-05 - Publisher: Courier Corporation

DOWNLOAD EBOOK

This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significan
Algebraic Equations
Language: en
Pages: 225
Authors: Edgar Dehn
Categories: Mathematics
Type: BOOK - Published: 2012-09-05 - Publisher: Courier Corporation

DOWNLOAD EBOOK

Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois
Algebraic Theories
Language: en
Pages: 268
Authors: J. Adámek
Categories: Mathematics
Type: BOOK - Published: 2010-11-18 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved
Algebraic Theories
Language: en
Pages: 269
Authors: J. Adámek
Categories: Mathematics
Type: BOOK - Published: 2010-11-18 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved