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" Acyclic models / "
Michael Barr.
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BL
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| Record Number
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846947
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| Main Entry
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Barr, Michael.
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| Title & Author
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Acyclic models /\ Michael Barr.
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, ©2002.
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| Series Statement
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CRM monograph series,; v. 17
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| Page. NO
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xi, 179 pages :: illustrations ;; 27 cm.
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| ISBN
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0821828770
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: 9780821828779
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| Bibliographies/Indexes
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Includes bibliographical references (pages 175-176) and index.
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| Contents
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Ch. 1. Categories -- 1. Introduction -- 2. Definition of category -- 3. Functors -- 4. Natural transformations -- 5. Elements and subobjects -- 6. The Yoneda Lemma -- 7. Pullbacks -- 8. Limits and colimits -- 9. Adjoint functors -- 10. Categories of fractions -- 11. The category of modules -- Ch. 2. Abelian Categories and Homological Algebra -- 1. Additive categories -- 2. Abelian categories -- 3. Exactness -- 4. Homology -- 5. Module categories -- 6. The Z construction -- Ch. 3. Chain Complexes and Simplicial Objects -- 1. Mapping cones -- 2. Contractible complexes -- 3. Simplicial objects -- 4. Associated chain complex -- 5. The Dold-Puppe theorem -- 6. Double complexes -- 7. Double simplicial objects -- 8. Homology and cohomology of a morphism -- Ch. 4. Triples a la Mode de Kan -- 1. Triples and cotriples -- 2. Model induced triples -- 3. Triples on the simplicial category -- 4. Historical Notes -- Ch. 5. The Main Acyclic Models Theorem -- 1. Acyclic classes -- 2. Properties of acyclic classes -- 3. The main theorem -- 4. Homotopy calculuses of fractions -- 5. Exactness conditions -- Ch. 6. Cartan-Eilenberg Cohomology -- 1. Beck modules -- 2. The main theorem -- 3. Groups -- 4. Associative algebras -- 5. Lie Algebras -- Ch. 7. Other Applications in Algebra -- 1. Commutative algebras -- 2. More on cohomology of commutative cohomology -- 3. Shukla cohomology -- 4. The Eilenberg-Zilber theorem -- Ch. 8. Applications in Topology -- 1. Singular homology -- 2. Covered spaces -- 3. Simplicial homology -- 4. Singular homology of triangulated spaces -- 5. Homology with ordered simplexes -- 6. Application to homology on manifolds.
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| Subject
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Acyclic models.
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Modèles acycliques.
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| Subject
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Acyclic models.
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Homologische Algebra
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Kategorientheorie
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| Dewey Classification
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512/.55
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| LC Classification
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QA169.B344 2002
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| NLM classification
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SK 320rvk
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