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[null,"1.","Record Nr.",null,"UNINA9910478880803321"]
[null,null,"Autore",null,"Duskin John Williford <1937->"]
[null,null,"Titolo",null,"Simplicial methods and the interpretation of \"triple\" cohomology / / J. Duskin"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , [1975]"]
[{"$nulls":4},"©1975"]
[null,null,"ISBN",null,"1-4704-0645-4"]
[null,null,"Descrizione fisica",null,"1 online resource (145 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; volume 3, issue 2, number 163 (November 1975)"]
[null,null,"Disciplina",null,"512/.55"]
[null,null,"Soggetti",null,"Categories (Mathematics)"]
[{"$nulls":4},"Triples, Theory of"]
[{"$nulls":4},"Complexes, Semisimplicial"]
[{"$nulls":4},"Homology theory"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"\"\"TABLE OF CONTENTS\"\"; \"\"ABSTRACT\"\"; \"\"DEDICATION\"\"; \"\"INTRODUCTION\"\"; \"\"0. SIMPLICIAL OBJECTS IN CATEGORIES\"\"; \"\"0.7 Verdier's Coskeleton Functor\"\"; \"\"0.8 Simplicial Kernels\"\"; \"\"0.11 Augmented Complexes (alternate descriptions)\"\"; \"\"0.12 Contractible and Split Complexes\"\"; \"\"0.13 The Augmented Coskeleton Functor\"\"; \"\"0.14 Stripping or Shift Functor Dec[sup(1)]\"\"; \"\"0.15 The Adjoint Pair (+,Dec[sup(1)])\"\"; \"\"0.17 Nerve of a Category\"\"; \"\"0.19 Homology and Cohomology\"\"; \"\"1. SIMPLICIAL AND COTRIPLE COHOMOLOGY\"\"; \"\"1.1 Cotriple Cohomology\"\"; \"\"1.2 Non-Homogeneous Complex\"\""]
[{"$nulls":4},"\"\"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??) )\"\""]
[{"$nulls":4},"\"\"3.8 Corollary (Homotopy Representability of H[sup(n)][sub(G)](X.â??) )\"\"; \"\"3.9 Definition of the n-th cohomology groupoid H[sup(n)](X.; "]
[{"$nulls":4},"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\"\""]
[{"$nulls":4},"\"\"6.2 Cocycle Formulae\"\"\"\"6.3 Twisted Product Algebra Defined By a 1-Cocycle\"\"; \"\"6.6.2 Alternative (Quotient) Construction of the Twisted Product Algebra Defined by a 1-cocycle\"\"; \"\"6.7 Construction of the Standard K(â??,n)-Torsor Above X Defined by an n-cocycle\"\"; \"\"6.8 Functor iality of S[sup(n)]( X; â??)\"\"; \"\"7. THE INTERPRETATION ADJUNCTIONS\"\"; \"\"7.2 The Canonical Map S[sup(n)](Z[sup(n)](X.)) â?? X.\"\"; \"\"7.7 Proof That the Canonical Map f : (S[sup(n)](Z[sup(n)](X.)))[sub(n-1)] â?? (X.)[sub(n-1)] Is a Morphism of â??-Algebras\"\"; \"\"8. THE INTERPRETATION BIJECTIONS (FIRST CONCLUSIONS)\"\""]
[{"$nulls":4},"\"\"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\"\""]