Triangulated Categories

Zusatztext "A very valuable source of information. . . . It is approachable and beautifully written. . . . I greatly enjoyed reading it." ---Tim Porter! Bulletin of the London Mathematical Society Informationen zum Autor Amnon Neeman Klappentext The first two chapters of this book offer a modern! self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple! elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research! providing! among other material! some remarkable improvements on Brown's classical representability theorem. In addition! the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated! and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra! algebraic geometry! homotopy theory! and mathematical physics. Zusammenfassung With the first two chapters of this book offering a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients, the author introduces a class of triangulated categories - the "well generated triangulated categories" - and studies their properties.

Product details

• Authors: Amnon Neeman, Amnon Stein, Neeman Amnon
• Assisted by: John N. Mather (Editor), Phillip Griffiths (Editor)
• Publisher: Princeton University Press
• Content: Book
• Product form: Paperback / Softback
• Publication date: 23.01.2001
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra
• EAN: 9780691086866
• ISBN: 978-0-691-08686-6
• Pages: 449
• Series: Annals of Mathematics Studies > 148; Annals of Mathematics Studies
• Subjects: Algebra, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Algebra / General, Axiom, Theorem, Algebraic Geometry, Homological algebra, cohomology, Abelian group, factorization, Yoneda Lemma, mathematical induction, homotopy, Universal Property, Prime number, Tensor Product, cardinality, Corollary, special case, derived category, transfinite induction, functor, Cardinal number, Diagram (category theory), Partially ordered set, Summation, Bijection, Duality (mathematics), Monomorphism, Isomorphism class, Open set, Basis (linear algebra), Existence theorem, Equivalence class, Linear Map, Existential quantification, Abelian category, Homotopy category, Natural transformation, Group homomorphism, Transfinite, Associative property, Counterexample, Subsequence, N0, Limit (category theory), Mapping cone (homological algebra), Spectral sequence, Discrete valuation ring, Direct sum, Adjoint functors, adjoint, Grothendieck's Tôhoku paper, Successor Ordinal, Coproduct, Grothendieck category, Functor category, Injective function, Subcategory, Limit ordinal, Homotopy colimit, Homotopy category of chain complexes, Projective object, Brown's representability theorem, Additive category, Category of abelian groups, Derived functor, Triangulated category, I0, Regular cardinal, Subobject, Quotient category, Injective object, Chain complex