Simplicial methods and the interpretation of "triple" cohomology / J. Duskin.

Format:

Book

Author/Creator:

Duskin, John Williford, 1937- author.

Series:

Memoirs of the American Mathematical Society ; number 163.

Memoirs of the American Mathematical Society ; volume 3, issue 2, number 163 (November 1975)

Language:

English

Subjects (All):

Categories (Mathematics).

Triples, Theory of.

Complexes, Semisimplicial.

Homology theory.

Physical Description:

1 online resource (145 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1975]

Language Note:

English

Contents:

""TABLE OF CONTENTS""; ""ABSTRACT""; ""DEDICATION""; ""INTRODUCTION""; ""0. SIMPLICIAL OBJECTS IN CATEGORIES""; ""0.7 Verdier's Coskeleton Functor""; ""0.8 Simplicial Kernels""; ""0.11 Augmented Complexes (alternate descriptions)""; ""0.12 Contractible and Split Complexes""; ""0.13 The Augmented Coskeleton Functor""; ""0.14 Stripping or Shift Functor Dec[sup(1)]""; ""0.15 The Adjoint Pair (+,Dec[sup(1)])""; ""0.17 Nerve of a Category""; ""0.19 Homology and Cohomology""; ""1. SIMPLICIAL AND COTRIPLE COHOMOLOGY""; ""1.1 Cotriple Cohomology""; ""1.2 Non-Homogeneous Complex""

""1.3 Triple Cohomology""""1.4 k-Boundary Systems""; ""1.5 Differential of a k-Boundary System and Cochain Reduction""; ""2. U-SPLIT AUGMENTED COMPLEXES AND THE STANDARD RESOLUTION""; ""2.6 k-Boundary System Defined by a U-Split Complex""; ""2.7 Naturality of k-Boundary Systems""; ""3. HOMOTOPY REPRESENTABILITY OF SIMPLICIAL AND COTRIPLE COHOMOLOGY

THE EILENBERG-MAC LANE COMPLEXES K(â??, n)""; ""3.1 Definition of the Complex L(â??,n)""; ""3.2 Definition of the Complex K(â??,n)""; ""3.7 Corollary (Homotopy Representability of H[sup(n)](X.; â??) )""

""3.8 Corollary (Homotopy Representability of H[sup(n)][sub(G)](X.â??) )""; ""3.9 Definition of the n-th cohomology groupoid H[sup(n)](X.; â??)""; ""4. K(â??,n)-T0RS0RS""; ""4.3 Morphisms of n-Torsors""; ""4.4 Change of Base""; ""4.5 Identification of K(â??,1)-torsors above X with principal â??-objects (i.e. â??-torsors) above X""; ""5. THE CHARACTERISTIC COCYCLE MAPPING Z[sup(n)][sub(G)]""; ""5.3 Functoriality of Z[sup(n)] on the Subcategory of Quasi-Coherent Morphisms""; ""6. STANDARD K(â??,n)-T0RS0R DEFINED BY AN n-COCYCLE""; ""6.1 The Standard Resolution of a â??-Algebra""

""6.2 Cocycle Formulae""""6.3 Twisted Product Algebra Defined By a 1-Cocycle""; ""6.6.2 Alternative (Quotient) Construction of the Twisted Product Algebra Defined by a 1-cocycle""; ""6.7 Construction of the Standard K(â??,n)-Torsor Above X Defined by an n-cocycle""; ""6.8 Functor iality of S[sup(n)]( X; â??)""; ""7. THE INTERPRETATION ADJUNCTIONS""; ""7.2 The Canonical Map S[sup(n)](Z[sup(n)](X.)) â?? X.""; ""7.7 Proof That the Canonical Map f : (S[sup(n)](Z[sup(n)](X.)))[sub(n-1)] â?? (X.)[sub(n-1)] Is a Morphism of â??-Algebras""; ""8. THE INTERPRETATION BIJECTIONS (FIRST CONCLUSIONS)""

""8.9 Theorem (Interpretation of Cotriple Cohomology)""""APPENDIX. TRIPLES, ALGEBRAS, AND TRIPLEABILITY""; ""A.2 Example: Triple Defined by a Pair of Adjoint Functors""; ""A.4 The Comparison Functor""; ""A.7 Properties""; ""A.8 Inverse Limits""; ""A.9 Tripleability Over (ENS)-Universal Algebras""; ""BIBLIOGRAPHY""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0645-4