Simplicial Methods and the Interpretation of ‘Triple’ Cohomology
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Table of Contents
Table of Contents
Simplicial Methods and the Interpretation of `Triple' Cohomology
- TABLE OF CONTENTS iii5
- ABSTRACT ii4 free
- DEDICATION v7 free
- INTRODUCTION 19 free
- 0. SIMPLICIAL OBJECTS IN CATEGORIES 816
- 0.7 Verdier's Coskeleton Functor 1018
- 0.8 Simplicial Kernels 1220
- 0.11 Augmented Complexes (alternate descriptions) 1422
- 0.12 Contractible and Split Complexes 1523
- 0.13 The Augmented Coskeleton Functor 1624
- 0.14 Stripping or Shift Functor Dec[sup(1)] 1826
- 0.15 The Adjoint Pair (+,Dec[sup(1)]) 1927
- 0.17 Nerve of a Category 2129
- 0.19 Homology and Cohomology 2533
- 1. SIMPLICIAL AND COTRIPLE COHOMOLOGY 2735
- 2. U-SPLIT AUGMENTED COMPLEXES AND THE STANDARD RESOLUTION 3947
- 3. H0M0T0PY REPRESENTABILITY OF SIMPLICIAL AND COTRIPLE COHOMOLOGY -- THE EILENBERG-MAC LANE COMPLEXES K(∏, n) 4957
- 4. K(∏,n)-T0RS0RS 6068
- 5. THE CHARACTERISTIC COCYCLE MAPPING Z[sup(n)][sub(G)] 9098
- 6. STANDARD K(∏,n)-T0RS0R DEFINED BY AN n-COCYCLE 96104
- 6.1 The Standard Resolution of a ∏-Algebra 98106
- 6.2 Cocycle Formulae 99107
- 6.3 Twisted Product Algebra Defined By a 1-Cocycle 100108
- 6.6.2 Alternative (Quotient) Construction of the Twisted Product Algebra Defined by a 1-cocycle 103111
- 6.7 Construction of the Standard K(∏,n)-Torsor Above X Defined by an n-cocycle 105113
- 6.8 Functor iality of S[sup(n)]( X;∏) 108116
- 7. THE INTERPRETATION ADJUNCTIONS 111119
- 8. THE INTERPRETATION BIJECTIONS (FIRST CONCLUSIONS) 120128
- APPENDIX. TRIPLES, ALGEBRAS, AND TRIPLEABILITY 125133
- BIBLIOGRAPHY 132140