04612nam 2200637 450 991081893880332120170918210016.01-4704-0645-4(CKB)3360000000464347(EBL)3113484(SSID)ssj0000973903(PQKBManifestationID)11542446(PQKBTitleCode)TC0000973903(PQKBWorkID)10984582(PQKB)11479709(MiAaPQ)EBC3113484(RPAM)327451(PPN)195410467(EXLCZ)99336000000046434720750619h19751975 uy| 0engur|n|---|||||txtccrSimplicial methods and the interpretation of "triple" cohomology /J. DuskinProvidence, Rhode Island :American Mathematical Society,[1975]©19751 online resource (145 p.)Memoirs of the American Mathematical Society ;volume 3, issue 2, number 163 (November 1975)Description based upon print version of record.0-8218-1863-5 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;number 163.Categories (Mathematics)Triples, Theory ofComplexes, SemisimplicialHomology theoryCategories (Mathematics)Triples, Theory of.Complexes, Semisimplicial.Homology theory.512/.55Duskin John Williford1937-1640652MiAaPQMiAaPQMiAaPQBOOK9910818938803321Simplicial methods and the interpretation of "triple" cohomology3984302UNINA