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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 construcΒ 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.

- Series:
**Grundlehren der mathematischen Wissenschaften 278** - Author:
**Michael Barr, Charles Wells (auth.)** - Year:
**1985** - Publisher:
**Springer-Verlag New York** - Language:
**English** - ISBN:
**978-1-4899-0023-4,978-1-4899-0021-0**

- File size:
**27 370 095** - Format:
**pdf**

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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...

The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads ...

Citing the old Indian story about the blind men feeling different parts of an elephant and coming up with divergent descriptions of the animal Johnstone (mathematics, U. of Cambridge, UK) says that topos theory can be described in divergent ways depending...

This book gives an elementary undergraduate-level introduction to Number Theory, with the emphasis on carefully explained proofs and worked examples; exercises (with solutions) are integrated into the text as part of the learning process. The first few ch...

With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/S...

The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads ...

This well-known booklet, now in its third, expanded edition, provides an informal survey of applications of singularity theory in a wide range of areas. Although the first few chapters touch briefly (and critically) on the Thom-Zeeman catastrophe theory, ...

This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working kno...

Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The sta...

This core text meets the needs of those involved in courses relating to the British political system. The author examines the institutions and practices of British government and politics and makes selective comparisons with the experience of other countr...

British Housebuilders is the first comprehensive account of the corporate history of the twentieth-century speculative housebuilding industry - the firms that `supplied` those houses and the entrepreneurs who created those firms.The transition from the lo...

An account of British foreign policy in the 20th century, discussing the challenging commitments, World Wars, Cold War and readjustments to the present day....

Barry Forshaw celebrates with enthusiasm the British horror film and its fascination for macabre cinema. A definitive study of the genre, British Gothic Cinema discusses the flowering of the field, with every key film discussed from its beginnings in the ...

This book reassesses the origins, development and legacy of the philosophy of the British idealists, demonstrating the enduring relevance of their thought for the modern discipline. This body of work coheres around the single unifying theme of the self β ...

The Congo Free State was under the personal rule of King Leopold II of the Belgians from 1885 to 1908. The accolades that attended its founding were soon contested by accusations of brutality, oppression, and murderous misrule, but the controversy, by its...