Triangulated Categories. (AM-148), Volume 148 /

Triangulated Categories. (AM-148), Volume 148 / / Amnon Neeman.

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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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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Neeman, Amnon,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2014]
©2001
Year of Publication:2014
Language:English
Series:Annals of Mathematics Studies ; 148
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Triangulated Categories. (AM-148), Volume 148 / Amnon Neeman.
Princeton, NJ : Princeton University Press, [2014]
©2001
1 online resource (449 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 148
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
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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 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.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Categories (Mathematics).
MATHEMATICS / Algebra / Abstract. bisacsh
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.
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502
print 9780691086866
https://doi.org/10.1515/9781400837212
https://www.degruyter.com/isbn/9781400837212
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language English
format eBook
author Neeman, Amnon,
Neeman, Amnon,
spellingShingle Neeman, Amnon,
Neeman, Amnon,
Triangulated Categories. (AM-148), Volume 148 /
Annals of Mathematics Studies ;
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
author_facet Neeman, Amnon,
Neeman, Amnon,
author_variant a n an
a n an
author_role VerfasserIn
VerfasserIn
author_sort Neeman, Amnon,
title Triangulated Categories. (AM-148), Volume 148 /
title_full Triangulated Categories. (AM-148), Volume 148 / Amnon Neeman.
title_fullStr Triangulated Categories. (AM-148), Volume 148 / Amnon Neeman.
title_full_unstemmed Triangulated Categories. (AM-148), Volume 148 / Amnon Neeman.
title_auth Triangulated Categories. (AM-148), Volume 148 /
title_alt 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
title_new Triangulated Categories. (AM-148), Volume 148 /
title_sort triangulated categories. (am-148), volume 148 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2014
physical 1 online resource (449 p.)
Issued also in print.
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
isbn 9781400837212
9783110494914
9783110442502
9780691086866
callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA169
callnumber-sort QA 3169 N446 42001EB
url https://doi.org/10.1515/9781400837212
https://www.degruyter.com/isbn/9781400837212
https://www.degruyter.com/document/cover/isbn/9781400837212/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 512 - Algebra
dewey-full 512.55
dewey-sort 3512 255
dewey-raw 512 .55
dewey-search 512 .55
doi_str_mv 10.1515/9781400837212
oclc_num 757993359
work_keys_str_mv AT neemanamnon triangulatedcategoriesam148volume148
status_str n
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carrierType_str_mv cr
hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
is_hierarchy_title Triangulated Categories. (AM-148), Volume 148 /
container_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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