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Algebraic Theories (Paperback, Softcover reprint of the original 1st ed. 1976): E. G. Manes Algebraic Theories (Paperback, Softcover reprint of the original 1st ed. 1976)
E. G. Manes
R1,487 Discovery Miles 14 870 Ships in 10 - 15 working days

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 fur Mathematik of the Eidgenossische Technische Hochschule in Zurich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zurich 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."

Foundations of System Theory: Finitary and Infinitary Conditions (Paperback, Softcover reprint of the original 1st ed. 1976):... Foundations of System Theory: Finitary and Infinitary Conditions (Paperback, Softcover reprint of the original 1st ed. 1976)
Brian Anderson, Michael A Arbib, E. G. Manes
R1,419 Discovery Miles 14 190 Ships in 10 - 15 working days

This paper is one of a series in which the ideas of category theory are applied to problems of system theory. As with the three principal earlier papers, [1-3], the emphasis is on study of the realization problem, or the problem of associating with an input-output description of a system an internal description with something analogous to a state-space. In this paper, several sorts of machines will be discussed, which arrange themselves in the following hierarchy: Input process Machine Output process (Tree automaton) Machine ~ ~ State-behavior Machine I Adjoint Machine .(Sequential Machine) ., I Decomposable Machine (Linear System, Group Machine) Each member of the hierarchy includes members below it; examples are included in parentheaes, and each example is at its lowest possible point in the hierarchy. There are contrived examples of output process machines and IV state-behavior machines which are not adjoint machines [3], but as yet, no examples with the accepted stature of linear systems [4], group machines [5, 6], sequential machines [7, Ch. 2], and tree automata [7, Ch. 4].

Category Theory Applied to Computation and Control - Proceedings of the First International Symposium, San Francisco, February... Category Theory Applied to Computation and Control - Proceedings of the First International Symposium, San Francisco, February 25-26, 1974 (Paperback, 1975 ed.)
E. G. Manes
R1,541 Discovery Miles 15 410 Ships in 10 - 15 working days
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