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Triangulated Categories. (AM-148), Volume 148

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their "ients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of t...

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Bibliographic Details
Main Author: Neeman, Amnon (Author)
Format: Electronic eBook
Language:English
Published: Princeton, NJ : Princeton University Press, [2014]
Series:Annals of Mathematics Studies ; 148
Subjects:
Categories (Mathematics).
MATHEMATICS / Algebra / Abstract.
Abelian category.
Abelian group.
Additive category.
Adjoint functors.
Adjoint.
Adjunction (field theory).
Associative property.
Axiom.
Basis (linear algebra).
Bijection.
Biproduct.
Brown's representability theorem.
Cardinal number.
Cardinality.
Category of abelian groups.
Chain complex.
Class (set theory).
Cohomology.
Computation.
Coproduct.
Corollary.
Countable set.
Counterexample.
Derived category.
Derived functor.
Diagram (category theory).
Direct limit.
Direct sum.
Discrete valuation ring.
Duality (mathematics).
Embedding.
Equivalence class.
Equivalence of categories.
Exact functor.
Exact sequence.
Existence theorem.
Existential quantification.
Factorization.
Finitely generated abelian group.
Functor category.
Functor.
Grothendieck category.
Grothendieck's Tôhoku paper.
Group homomorphism.
Homological algebra.
Homotopy category of chain complexes.
Homotopy category.
Homotopy colimit.
Homotopy.
I0.
Injective function.
Injective object.
Integer.
Isomorph.
Isomorphism class.
Jack Morava.
K-theory.
Limit (category theory).
Limit of a sequence.
Limit ordinal.
Linear map.
Mapping cone (homological algebra).
Mathematical induction.
Maximal ideal.
Module (mathematics).
Monomorphism.
Moore space.
Morphism.
N0.
Natural transformation.
Open set.
Partially ordered set.
Pierre Deligne.
Prime number.
Projective object.
Proportionality (mathematics).
Quotient category.
Regular cardinal.
Representable functor.
Sheaf (mathematics).
Special case.
Spectral sequence.
Subcategory.
Subobject.
Subsequence.
Subset.
Successor ordinal.
Summation.
Tautology (logic).
Tensor product.
Theorem.
Theory.
Topological group.
Transfinite induction.
Transfinite.
Triangulated category.
Universal property.
Vector space.
Vladimir Voevodsky.
Yoneda lemma.
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Table of Contents:
  • Frontmatter
  • Contents
  • 0. Acknowledgements
  • 1. Introduction
  • Chapter 1. Definition and elementary properties of triangulated categories
  • Chapter 2. Triangulated functors and localizations of triangulated categories
  • Chapter 3. Perfection of classes
  • Chapter 4. Small objects, and Thomason's localisation theorem
  • Chapter 5. The category A(S)
  • Chapter 6. The category Εx (Sop, Ab)
  • Chapter 7. Homological properties of Εx(Sop,Αb)
  • Chapter 8. Brown representability
  • Chapter 9. Bousfield localisation
  • Appendix A. Abelian categories
  • Appendix B. Homological functors into [AB5α] categories
  • Appendix C. Counterexamples concerning the abelian category A(Τ)
  • Appendix D. Where Τ is the homotopy category of spectra
  • Appendix E. Examples of non-perfectly-generated categories
  • Bibliography
  • Index

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