Table of contents for Methods of homological algebra / Sergei I. Gelfand, Yuri I. Manin.


Bibliographic record and links to related information available from the Library of Congress catalog. Note: Electronic data is machine generated. May be incomplete or contain other coding.


Counter




I.  Simplicial  Sets  ............................................  1
    1.1  Triangulated  Spaces  ....................................  1
    1.2  Simplicial Sets .........................................  6
    1.3  Simplicial Topological Spaces and the
         Eilenberg-Zilber Theorem ............................... 17
    1.4  Homology and Cohomology .............................. 23
    1.5  Sheaves ............................................... 31
    1.6  The Exact Sequence .................................... 40
    1.7  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 A-Modules...... 267
    IV.4 Cores  .................................................  278



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





Library of Congress Subject Headings for this publication:Algebra, Homological