Toposes, Triples and Theories
Seiten
2013
|
Softcover reprint of the original 1st ed. 1985
Springer-Verlag New York Inc.
978-1-4899-0023-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4899-0023-4 (ISBN)
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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 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.
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.
1. Categories.- 2. Toposes.- 3. Triples.- 4. Theories.- 5. Properties of Toposes.- 6. Permanence Properties of Toposes.- 7. Representation Theorems.- 8. Cocone Theories.- 9. More on Triples.- Index to Exercises.
| Reihe/Serie | Grundlehren der mathematischen Wissenschaften ; .278 |
|---|---|
| Zusatzinfo | black & white illustrations |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 511 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4899-0023-3 / 1489900233 |
| ISBN-13 | 978-1-4899-0023-4 / 9781489900234 |
| Zustand | Neuware |
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