Algebraic Theories
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Algebraic Theories
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Author : E.G. Manes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Theories written by E.G. Manes 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 2012-12-06 with Mathematics categories.
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
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Author : J. Adámek
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-18
Algebraic Theories written by J. Adámek 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 2010-11-18 with Mathematics categories.
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 very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.
Algebraic Theories
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Author : Leonard Dickson
language : en
Publisher: Courier Corporation
Release Date : 2014-03-05
Algebraic Theories written by Leonard Dickson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-05 with Mathematics categories.
This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. Algebraic Theories studies all of the important theories; its extensive offerings range from the foundations of higher algebra and the Galois theory of algebraic equations to finite linear groups (including Klein's "icosahedron" and the theory of equations of the fifth degree) and algebraic invariants. The full treatment includes matrices, linear transformations, elementary divisors and invariant factors, and quadratic, bilinear, and Hermitian forms, both singly and in pairs. The results are classical, with due attention to issues of rationality. Elementary divisors and invariant factors receive simple, natural introductions in connection with the classical form and a rational, canonical form of linear transformations. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications.
Algebraic Theories
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Author : E. G. Manes
language : en
Publisher:
Release Date : 1976-07-15
Algebraic Theories written by E. G. Manes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-07-15 with categories.
Modern Algebraic Theories
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Author : Leonard Eugene Dickson
language : en
Publisher:
Release Date : 1926
Modern Algebraic Theories written by Leonard Eugene Dickson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1926 with Algebra categories.
Algebraic Theories
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Author : Leonard Eugene Dickson
language : en
Publisher:
Release Date : 1926
Algebraic Theories written by Leonard Eugene Dickson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1926 with Algebraic number theory categories.
The Skeleton Key Of Mathematics
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Author : D. E. Littlewood
language : en
Publisher: Courier Corporation
Release Date : 2013-12-31
The Skeleton Key Of Mathematics written by D. E. Littlewood and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
Straightforward explanation of abstract principles common to science and math, including Euclid's algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; Galois theory; algebraic geometry; more.
Algebraic Theory Of Automata Networks
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Author : Pal Domosi
language : en
Publisher: SIAM
Release Date : 2005-01-01
Algebraic Theory Of Automata Networks written by Pal Domosi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
This book investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories.
Introduction To Algebraic Theories
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Author : Adrian Albert A.
language : en
Publisher: Maine Press
Release Date : 2007-03
Introduction To Algebraic Theories written by Adrian Albert A. and has been published by Maine Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03 with Mathematics categories.
PREFACE. THE Author of this very practical treatise on Scotch Loch - Fishing desires clearly that it may be of use to all who had it. He does not pretend to have written anything new, but to have attempted to put what he has to say in as readable a form as possible. Everything in the way of the history and habits of fish has been studiously avoided, and technicalities have been used as sparingly as possible. The writing of this book has afforded him pleasure in his leisure moments, and that pleasure would be much increased if he knew that the perusal of it would create any bond of sympathy between himself and the angling community in general. This section is interleaved with blank shects for the readers notes. The Author need hardly say that any suggestions addressed to the case of the publishers, will meet with consideration in a future edition. We do not pretend to write or enlarge upon a new subject. Much has been said and written-and well said and written too on the art of fishing but loch-fishing has been rather looked upon as a second-rate performance, and to dispel this idea is one of the objects for which this present treatise has been written. Far be it from us to say anything against fishing, lawfully practised in any form but many pent up in our large towns will bear us out when me say that, on the whole, a days loch-fishing is the most convenient. One great matter is, that the loch-fisher is depend- ent on nothing but enough wind to curl the water, -and on a large loch it is very seldom that a dead calm prevails all day, -and can make his arrangements for a day, weeks beforehand whereas the stream- fisher is dependent for a good take on the state of the water and however pleasant and easy it may be for one living near the banks of a good trout stream or river, it is quite another matter to arrange for a days river-fishing, if one is looking forward to a holiday at a date some weeks ahead. Providence may favour the expectant angler with a good day, and the water in order but experience has taught most of us that the good days are in the minority, and that, as is the case with our rapid running streams, -such as many of our northern streams are, -the water is either too large or too small, unless, as previously remarked, you live near at hand, and can catch it at its best. A common belief in regard to loch-fishing is, that the tyro and the experienced angler have nearly the same chance in fishing, -the one from the stern and the other from the bow of the same boat. Of all the absurd beliefs as to loch-fishing, this is one of the most absurd. Try it. Give the tyro either end of the boat he likes give him a cast of ally flies he may fancy, or even a cast similar to those which a crack may be using and if he catches one for every three the other has, he may consider himself very lucky. Of course there are lochs where the fish are not abundant, and a beginner may come across as many as an older fisher but we speak of lochs where there are fish to be caught, and where each has a fair chance. Again, it is said that the boatman has as much to do with catching trout in a loch as the angler. Well, we dont deny that. In an untried loch it is necessary to have the guidance of a good boatman but the same argument holds good as to stream-fishing...
Introduction To Algebraic Theories
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Author : Abraham Adrian Albert
language : en
Publisher:
Release Date : 1941
Introduction To Algebraic Theories written by Abraham Adrian Albert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1941 with Algebraic fields categories.
