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Bibliographic Details
Main Authors:	Gelʹfand, Sergej I. 1944- (Author), Manin, Jurij I. 1937-2023 (Author)
Format:	Book
Language:	English Russian
Published:	Berlin [u.a.] Springer 2003
Edition:	2. ed.
Series:	Springer monographs in mathematics
Subjects:	Algèbre homologique Homologische algebra Algebra, Homological Homologische Algebra
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010049556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XX, 372 S. graph. Darst.
ISBN:	9783540435839 3540435832

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Record in the Search Index

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adam_text	CONTENTS I. SIMPLICIAL SETS ............................................ 1 I.1 TRIANGULATED SPACES .................................... 1 I.2 SIMPLICIAL SETS ......................................... 6 I.3 SIMPLICIAL TOPOLOGICAL SPACES AND THE EILENBERGZILBER THEOREM ............................... 17 I.4 HOMOLOGY AND COHOMOLOGY .............................. 23 I.5 SHEAVES ............................................... 31 I.6 THE EXACT SEQUENCE .................................... 40 I.7 COMPLEXES ............................................. 46 II. MAIN NOTIONS OF THE CATEGORY THEORY .................... 57 II.1 THE LANGUAGE OF CATEGORIES AND FUNCTORS ................. 57 II.2 CATEGORIES AND STRUCTURES, EQUIVALENCE OF CATEGORIES ........ 69 II.3 STRUCTURES AND CATEGORIES. REPRESENTABLE FUNCTORS .......... 78 II.4 CATEGORY APPROACH TO THE CONSTRUCTION OF GEOMETRICAL OBJECTS .................................. 93 II.5 ADDITIVE AND ABELIAN CATEGORIES ......................... 109 II.6 FUNCTORS IN ABELIAN CATEGORIES ........................... 122 III. DERIVED CATEGORIES AND DERIVED FUNCTORS ................. 139 III.1 COMPLEXES AS GENERALIZED OBJECTS ........................ 139 III.2 DERIVED CATEGORIES AND LOCALIZATION ...................... 144 III.3 TRIANGLES AS GENERALIZED EXACT TRIPLES .................... 153 III.4 DERIVED CATEGORY AS THE LOCALIZATION OF HOMOTOPIC CATEGORY 159 III.5 THE STRUCTURE OF THE DERIVED CATEGORY .................... 164 III.6 DERIVED FUNCTORS ....................................... 185 III.7 DERIVED FUNCTOR OF THE COMPOSITION. SPECTRAL SEQUENCE ..... 200 III.8 SHEAF COHOMOLOGY ...................................... 218 IV. TRIANGULATED CATEGORIES .................................. 239 IV.1 TRIANGULATED CATEGORIES ................................. 239 IV.2 DERIVED CATEGORIES ARE TRIANGULATED . . . . . . . . . . . . . . . . . . . . . . 251 IV.3 AN EXAMPLE: THE TRIANGULATED CATEGORY OF -MODULES ...... 267 IV.4 CORES ................................................. 278 XX CONTENTS V. INTRODUCTION TO HOMOTOPIC ALGEBRA ....................... 291 V.1 CLOSED MODEL CATEGORIES ................................ 291 V.2 HOMOTOPIC CHARACTERIZATION OF WEAK EQUIVALENCES .......... 299 V.3 DG -ALGEBRAS AS A CLOSED MODEL CATEGORY ................. 333 V.4 MINIMAL ALGEBRAS ...................................... 342 V.5 EQUIVALENCE OF HOMOTOPY CATEGORIES ...................... 352 REFERENCES .................................................... 357 INDEX ......................................................... 369
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author	Gelʹfand, Sergej I. 1944- Manin, Jurij I. 1937-2023
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indexdate	2024-12-20T11:08:59Z
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isbn	9783540435839 3540435832
language	English Russian
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spellingShingle	Gelʹfand, Sergej I. 1944- Manin, Jurij I. 1937-2023 Methods of homological algebra Algèbre homologique Homologische algebra gtt Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd
subject_GND	(DE-588)4160598-6
title	Methods of homological algebra
title_alt	Metody gomologičeskoj algebry
title_auth	Methods of homological algebra
title_exact_search	Methods of homological algebra
title_full	Methods of homological algebra Sergei I. Gelfand ; Yuri I. Manin
title_fullStr	Methods of homological algebra Sergei I. Gelfand ; Yuri I. Manin
title_full_unstemmed	Methods of homological algebra Sergei I. Gelfand ; Yuri I. Manin
title_short	Methods of homological algebra
title_sort	methods of homological algebra
topic	Algèbre homologique Homologische algebra gtt Algebra, Homological Homologische Algebra (DE-588)4160598-6 gnd
topic_facet	Algèbre homologique Homologische algebra Algebra, Homological Homologische Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010049556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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