Toposes, Triples, and Theories by M Barr

Toposes, Triples, and Theories by M Barr

As its title suggests, this book is an introduction to three ideas and the connections between them. Before describing the content of the book in detail, we describe each concept briefly. More extensive introductory descriptions of each concept are in the introductions and notes to Chapters 2, 3 and 4. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. In that sense, a topos is a generalized set theory. However, it originated with Grothendieck and Giraud as an abstraction of the of the category of sheaves of sets on a topological space. Later, properties Lawvere and Tierney introduced a more general id~a which they called "elementary topos" (because their axioms did not quantify over sets), and they and other mathematicians developed the idea that a theory in the sense of mathematical logic can be regarded as a topos, perhaps after a process of completion. The concept of triple originated (under the name "standard construc- in Godement's book on sheaf theory for the purpose of computing tions") sheaf cohomology. Then Peter Huber discovered that triples capture much of the information of adjoint pairs. Later Linton discovered that triples gave an equivalent approach to Lawverc's theory of equational theories (or rather the infinite generalizations of that theory). Finally, triples have turned out to be a very important tool for deriving various properties of toposes.

From the reviews: "Michael Barr, Charles Wells uses the most efficient tools to get at the central theoremsThis is a very readable introduction to the subject ... . no other book goes as concisely and comprehensively to all the aspects of toposes as this one. Category theory, algebra, logic, arithmetic, geometry, and cohomology all come in, in a well chosen perspective. ... it remains the best single text on the subject." (Wordtrade, 2008)

SKU	Nicht verfügbar
ISBN 13	9780387961156
Titel	Toposes, Triples, and Theories
Autor	M Barr
Serie	Grundlehren Der Mathematischen Wissenschaften
Buchzustand	Nicht verfügbar
Verlag	Springer-Verlag New York Inc.
Erscheinungsjahr	1984-12-20
Seitenanzahl	347
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar